# Department. of Mathematics and Statistics

## Department of Mathematics and Statistics

**Name of Department: **

Department of Mathematics and Statistics

**Name of Ag. Head Of Department:**

Dr. P. C. Jakreece

**Contact E-mail: **

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**Contact Phone Number(s): **

08038703131

I

**NTRODUCTION**The Department of Mathematics and Statistics offers a broad integrated programme of studies in Mathematical disciplines.

The first two years of the structured programme afford each student the maximum opportunity to develop the knowledge, skills, attitudes that will best motivate and equip him/her to choose the field of endeavor most appropriate to his or her talents. Basic Mathematics knowledge and skills are emphasized at that level. In the last two years each student concentrates on one of the five areas: Mathematics, Statistics, Mathematics/Statistics, Mathematics/Computer Science, and Statistics/Computer Science.

Objective

The programmes are designed to equip graduates for a wide variety of careers in the Mathematical disciplines. The main objectives are as follows:

(i) To solve the manpower needs of the immediate environment in particular and the nation in general as regards the disciplines of Mathematics, Statistics and Computer Science.

The programmes are designed to equip graduates for a wide variety of careers in the Mathematical disciplines. The main objectives are as follows:

(i) To solve the manpower needs of the immediate environment in particular and the nation in general as regards the disciplines of Mathematics, Statistics and Computer Science.

(ii) To prepare students for employment in establishment and industries and for research and graduate studies in these disciplines.

The applicability of these disciplines in the modern industrial environment is highly emphasized. As industries nowadays depend heavily on the use of computers for aspects of their day-to-day operations, the Mathematics and Statistics programme is tailored to developing computing skills that will enable the graduates to fit into the modern industrial environment. The Mathematics/Statistics programmes, as well as stressing traditional methods, also incorporates new computer-based techniques and popular statistical softwares. Consequently Student Industrial Work Experience Scheme (SIWES) is emphasized for students in the department.

The applicability of these disciplines in the modern industrial environment is highly emphasized. As industries nowadays depend heavily on the use of computers for aspects of their day-to-day operations, the Mathematics and Statistics programme is tailored to developing computing skills that will enable the graduates to fit into the modern industrial environment. The Mathematics/Statistics programmes, as well as stressing traditional methods, also incorporates new computer-based techniques and popular statistical softwares. Consequently Student Industrial Work Experience Scheme (SIWES) is emphasized for students in the department.

Curriculum

The curriculum for the BSc. Degree programmes in the Department consists of two sections namely the introductory and the advanced sections. The introductory section consists of foundation courses which are taken by all the students of the department and it extends over the first four semester of the four-year degree programme. The foundations courses seek to provide a strong grounding in Mathematics and basic sciences.

The curriculum for the BSc. Degree programmes in the Department consists of two sections namely the introductory and the advanced sections. The introductory section consists of foundation courses which are taken by all the students of the department and it extends over the first four semester of the four-year degree programme. The foundations courses seek to provide a strong grounding in Mathematics and basic sciences.

The advanced part of the degree programme commences from the first semester of year three. The department offers five streams of courses and students can choose any of them. The following are the programmes:

(i) Mathematics (Pure and Applied)

(ii) Statistics

(iii) Mathematics/Statistics

(iv) Mathematics/Computer Science

(v) Statistics/Computer Science

(i) Mathematics (Pure and Applied)

(ii) Statistics

(iii) Mathematics/Statistics

(iv) Mathematics/Computer Science

(v) Statistics/Computer Science

**Departmental Entry Requirements**

The minimum requirement for entry into a Bachelor Degree program in the Department is the SSSC or WASC or GCE O/L or the equivalent with credits (in at most two sittings) in English, Mathematics, Physics, Chemistry and one other subject, depending on the sub-programme of study. Candidates for B.Sc. Mathematics, Statistics Mathematics/Statistics, Statistics and Computer programmes require credit in Biology or Economics or Geography while candidates for B.Sc. Mathematics/Computer Science programmes require credit in Biology. Attention of each student is drawn to the document “Statement of Academic Polices” of the University of Port Harcourt general entry requirements.

Eligibility to Graduate

Students are eligible to graduate upon completion of the prescribed courses for the relevant programme including Research project, with a minimum Cumulative Grade Point Average (CGPA) OF 1.50. Computations of CGPA as well as other matters relating to students status and eligibility to graduate can be obtained from Statement of Academic Policies of the University of Port Harcourt.

Students are eligible to graduate upon completion of the prescribed courses for the relevant programme including Research project, with a minimum Cumulative Grade Point Average (CGPA) OF 1.50. Computations of CGPA as well as other matters relating to students status and eligibility to graduate can be obtained from Statement of Academic Policies of the University of Port Harcourt.

Withdrawal and Academic Probation

A student whose CGPA falls below 1.00 at the end of an academic year will be placed on probation in the subsequent year and will be restricted to carry credit load of 15 to 18units. A student will be required to withdraw from a programme if the CGPA is below an approved minimum of 1.00 after a period of probation.

Auditing of Courses

Students may take courses outside their proscribed programmes. The courses shall be recorded in their transcripts. However audited courses shall not be used in calculating the CGPA.

A student whose CGPA falls below 1.00 at the end of an academic year will be placed on probation in the subsequent year and will be restricted to carry credit load of 15 to 18units. A student will be required to withdraw from a programme if the CGPA is below an approved minimum of 1.00 after a period of probation.

Auditing of Courses

Students may take courses outside their proscribed programmes. The courses shall be recorded in their transcripts. However audited courses shall not be used in calculating the CGPA.

Academic Advisers

Every student is attached to an Academic Adviser who is a member of the academic staff of the department and who will advise him/her on academic affairs as well as on personal matter where necessary. Academic Advises are expected to follow their students’ academic progresses and provide counseling to them. It is the duty of the Head of Department to assign an Academic Adviser to each student at the beginning of each academic session.

Every student is attached to an Academic Adviser who is a member of the academic staff of the department and who will advise him/her on academic affairs as well as on personal matter where necessary. Academic Advises are expected to follow their students’ academic progresses and provide counseling to them. It is the duty of the Head of Department to assign an Academic Adviser to each student at the beginning of each academic session.

Department of Mathematics and Statistics

GES 100.1 Communication Skill in English

The course seeks to develop in the students a well informed attitude to the English Language and to equip them with the knowledge of English communication and study skill that will facilitate their work in the University and beyond.

The course seeks to develop in the students a well informed attitude to the English Language and to equip them with the knowledge of English communication and study skill that will facilitate their work in the University and beyond.

MTH 110.1 Algebra And Trigonometry

Elementary notions of sets, Subsets, Union, Intersection, Compliments, Venn Diagrams. Real Numbers Integers, rational and Irrationals, Mappings of a set. Real functions and their compositions. Quadratic functions. Cubic function, Roots of quadratic and cubic functions. Partial fractions. Equations with complex roots. Complex number. Geometric representation of complex numbers, De Moirvers, Series and sequences. Principle of mathematical induction, Binomial theorem. Trigonometry functions of angles. Circular function. Addition Theorems. Double and half angles.

Elementary notions of sets, Subsets, Union, Intersection, Compliments, Venn Diagrams. Real Numbers Integers, rational and Irrationals, Mappings of a set. Real functions and their compositions. Quadratic functions. Cubic function, Roots of quadratic and cubic functions. Partial fractions. Equations with complex roots. Complex number. Geometric representation of complex numbers, De Moirvers, Series and sequences. Principle of mathematical induction, Binomial theorem. Trigonometry functions of angles. Circular function. Addition Theorems. Double and half angles.

MTH 120.1 Calculus

Function of a real variable, graphs, limits and idea of continuity. The derivative as limit of rate of change. Technique of differentiation. Extreme curve sketching; integration as an inverse of differentiation. Methods of integration. Definite integrals. Application to areas, volumes.

Function of a real variable, graphs, limits and idea of continuity. The derivative as limit of rate of change. Technique of differentiation. Extreme curve sketching; integration as an inverse of differentiation. Methods of integration. Definite integrals. Application to areas, volumes.

STA 190.1 Lab for Descriptive Statistics

Use of Statistical softwares (eg. SPSS, Minitab, Gretl, Statgrahics and Micro-Excel). Data Imputation, Sorting and Ranking, Graphical Summary and Interpretation. Summarizing and Inspection of Data using Tables and Graphical methods.

Charts: Pie Simple, Component, Multiple bar charts etc.

Diagrams: Tree, Stem-and-Leaf, Box-and-Whisker etc.

Graphs: Histogram, frequency polygon, cumulative frequency distribution (Ogive), line graphs etc.

Methods of Data Collection (primary and secondary): (1) Use of Questionnaire (Collation, Coding, Tabulation and Presentation). (2) from existing (published or unpublished) sources

Computation: Measures of Central Tendency (location): Arithmetic, Geometric and Harmonic Means, Mode Median, Quartiles etc. Measures of Variation: Range, Variance, Standard deviation, Coefficient of Variation (Grouped and Ungrouped) etc. Measures of Symmetry: Skewness and Kurtosis. Etc. Weighted Arithmetic Mean: Mean and Variance of Two or More Distributions, Combined Variance and the combined mean can be ignored.

Data following a normal distribution: Anderson-Darling Normality test, Kolmogorov-Smirnor test, Ryan-Joiner test and Jarque-Bera (JB) test.

Use of Statistical softwares (eg. SPSS, Minitab, Gretl, Statgrahics and Micro-Excel). Data Imputation, Sorting and Ranking, Graphical Summary and Interpretation. Summarizing and Inspection of Data using Tables and Graphical methods.

Charts: Pie Simple, Component, Multiple bar charts etc.

Diagrams: Tree, Stem-and-Leaf, Box-and-Whisker etc.

Graphs: Histogram, frequency polygon, cumulative frequency distribution (Ogive), line graphs etc.

Methods of Data Collection (primary and secondary): (1) Use of Questionnaire (Collation, Coding, Tabulation and Presentation). (2) from existing (published or unpublished) sources

Computation: Measures of Central Tendency (location): Arithmetic, Geometric and Harmonic Means, Mode Median, Quartiles etc. Measures of Variation: Range, Variance, Standard deviation, Coefficient of Variation (Grouped and Ungrouped) etc. Measures of Symmetry: Skewness and Kurtosis. Etc. Weighted Arithmetic Mean: Mean and Variance of Two or More Distributions, Combined Variance and the combined mean can be ignored.

Data following a normal distribution: Anderson-Darling Normality test, Kolmogorov-Smirnor test, Ryan-Joiner test and Jarque-Bera (JB) test.

STA 160.1 Descriptive Statistics

Essence of Statistics. Statistical data: types, sources and methods of collection. Presentation of data: tables chart and graphs. Charts: Pie Simple, Component, Multiple bar charts etc.

Diagrams: Tree, Stem-and-Leaf, Box-and-Whisker etc. Graphs: Histogram, frequency polygon, cumulative frequency distribution (Ogive), line graphs etc. Statistical Notations. Errors and Approximations. Frequency and cumulative distributions, Measures of Central Tendency (location): Arithmetic, Geometric and Harmonic Means, Mode Median, Quartiles etc. Measures of Variation: Range, Variance, Standard deviation, etc. Measures of Symmetry: Skewness and Kurtosis. etc.

Essence of Statistics. Statistical data: types, sources and methods of collection. Presentation of data: tables chart and graphs. Charts: Pie Simple, Component, Multiple bar charts etc.

Diagrams: Tree, Stem-and-Leaf, Box-and-Whisker etc. Graphs: Histogram, frequency polygon, cumulative frequency distribution (Ogive), line graphs etc. Statistical Notations. Errors and Approximations. Frequency and cumulative distributions, Measures of Central Tendency (location): Arithmetic, Geometric and Harmonic Means, Mode Median, Quartiles etc. Measures of Variation: Range, Variance, Standard deviation, etc. Measures of Symmetry: Skewness and Kurtosis. etc.

PHY 101.1 Introduction of Mechanics and Properties of Matter

Topics covered in this course will include the following:- Motion in one dimension, motion in a plane, work and energy, conservation laws, collision, solid friction, rotational kinematics and rotational dynamics, equilibrium of rigid bodies, oscillations, gravitation, fluid statics and fluid dynamics. Surface Tension, Viscosity and Hydrostatics.

Topics covered in this course will include the following:- Motion in one dimension, motion in a plane, work and energy, conservation laws, collision, solid friction, rotational kinematics and rotational dynamics, equilibrium of rigid bodies, oscillations, gravitation, fluid statics and fluid dynamics. Surface Tension, Viscosity and Hydrostatics.

PHY 102.1 Laboratory Practice I

This course emphasizes experimental verification and quantitative measurements of physical laws, treatment of measurement errors and graphical analysis. The experiments include studies of mechanical systems, static and rotational dynamics of rigid bodies, viscosity, elasticity, surface tension and hydrostatics.

This course emphasizes experimental verification and quantitative measurements of physical laws, treatment of measurement errors and graphical analysis. The experiments include studies of mechanical systems, static and rotational dynamics of rigid bodies, viscosity, elasticity, surface tension and hydrostatics.

CHM 130.1 General Chemistry I

Basic principles of matter and energy from the chemist’s point of view. A broadly based course suitable for students from various schools as well as those from the Faculty of Science. Topics to be covered will include atomic theory and molecular structure, stoichiometry, the periodic classification of the elements, atomic structure, chemical bonding, properties of gases, solids, liquids and solutions, chemical equilibrium, Ionic equilibrium, chemical thermodynamics, electrochemistry and chemicals kinetics.

Basic principles of matter and energy from the chemist’s point of view. A broadly based course suitable for students from various schools as well as those from the Faculty of Science. Topics to be covered will include atomic theory and molecular structure, stoichiometry, the periodic classification of the elements, atomic structure, chemical bonding, properties of gases, solids, liquids and solutions, chemical equilibrium, Ionic equilibrium, chemical thermodynamics, electrochemistry and chemicals kinetics.

GES 102.1 Introduction to Logic and Philosophy

A brief survey of the scope, notions, branches and problems of philosophy symbolic logic, specific symbolic logic, specific symbolic logic, specific symbols in symbolic logic. Conjunction, affirmation, negations, disjunction, equivalence and conditional statements. Law of thought. The method of deduction, using rule of inference and bi-conditions. Quantitative theory.

A brief survey of the scope, notions, branches and problems of philosophy symbolic logic, specific symbolic logic, specific symbolic logic, specific symbols in symbolic logic. Conjunction, affirmation, negations, disjunction, equivalence and conditional statements. Law of thought. The method of deduction, using rule of inference and bi-conditions. Quantitative theory.

GES 101.2 Computer Appreciation and Applications

History of Computers, Generation and Classification of computers; IPO model of a computer Components of a computer system-Hardwares and Softwares; Programming Language, Organization of Data; Data Computer techniques; Introduction to Computer Networks; Software and its applications; Use of Key board as an input device; DOS Windows, Word processing Spreadsheets; Application of Computers in Medicne, Social Sciences, humanities, Education and Management Sciences.

History of Computers, Generation and Classification of computers; IPO model of a computer Components of a computer system-Hardwares and Softwares; Programming Language, Organization of Data; Data Computer techniques; Introduction to Computer Networks; Software and its applications; Use of Key board as an input device; DOS Windows, Word processing Spreadsheets; Application of Computers in Medicne, Social Sciences, humanities, Education and Management Sciences.

GES 103.2 Nigerian People and Culture

The overall objective of this course is to help students understand the concept of culture and its relevant to human society especially as it relates to development. In more specific terms, the course will be designed to help the students know the history of various Nigerian cultures beginning with pre-colonial Nigeria society. Colonialism constitutes a vital watershed in Nigerian history. This the course will

1. Identify the influence of colonialism on Nigerian culture.

2. Focus on contemporary Nigerian culture explaining issues that relate to the political, economic, educational, religious and social institutions in the nation.

The course outline includes: the concept of culture

The overall objective of this course is to help students understand the concept of culture and its relevant to human society especially as it relates to development. In more specific terms, the course will be designed to help the students know the history of various Nigerian cultures beginning with pre-colonial Nigeria society. Colonialism constitutes a vital watershed in Nigerian history. This the course will

1. Identify the influence of colonialism on Nigerian culture.

2. Focus on contemporary Nigerian culture explaining issues that relate to the political, economic, educational, religious and social institutions in the nation.

The course outline includes: the concept of culture

PHY 112.2 Introduction to Electricity and Magnetism. This is the introductory course on Electricity and Magnetism. Topics covered will include:-

the Electric field, Gauss’s Law Electric potential, Capacitors and Dielectric, current and resistance, electromotive force and circuits, the magnetic field, Ampere’s Law, Faraday’s Law of induction.

the Electric field, Gauss’s Law Electric potential, Capacitors and Dielectric, current and resistance, electromotive force and circuits, the magnetic field, Ampere’s Law, Faraday’s Law of induction.

PHY 103.2 Laboratory Practice II

The experiment carried out in this course will cover areas discussed in PHY 1122.Tes experiments include verifications of the current electricity, measurement of the electrical properties of conductors, d.c. and a.c. circuit properties, series and parallel resonant circuits, transformer characteristics and other electrical

The experiment carried out in this course will cover areas discussed in PHY 1122.Tes experiments include verifications of the current electricity, measurement of the electrical properties of conductors, d.c. and a.c. circuit properties, series and parallel resonant circuits, transformer characteristics and other electrical

CHM 131.2 General Chemistry II

Application of the principles of chemical and physical change to the study of the behavior of matter and the interaction between matter. Course content includes:- the chemistry of the representative elements and their common compounds with emphasis on graduation of their properties, brief chemistry of the first series of transition elements, general principles of extraction of metals, introductory nuclear chemistry.

Application of the principles of chemical and physical change to the study of the behavior of matter and the interaction between matter. Course content includes:- the chemistry of the representative elements and their common compounds with emphasis on graduation of their properties, brief chemistry of the first series of transition elements, general principles of extraction of metals, introductory nuclear chemistry.

MTH 124.2 Coordinate Geometry

Straight lines, circles, parabola, ellipse, hyperbola. Tangents, normal. Addition of Vectors. Scalar and Vector products. Vector equation of a line and place. Kinematics of a particle. Components of velocity and acceleration of a particle moving in a plane. Force, momentum, laws of motion, under gravity projectiles, resisted vertical motion, elastic string, simple pendulum impulse. Impact of two smooth spheres. Addition of Vectors

Straight lines, circles, parabola, ellipse, hyperbola. Tangents, normal. Addition of Vectors. Scalar and Vector products. Vector equation of a line and place. Kinematics of a particle. Components of velocity and acceleration of a particle moving in a plane. Force, momentum, laws of motion, under gravity projectiles, resisted vertical motion, elastic string, simple pendulum impulse. Impact of two smooth spheres. Addition of Vectors

MTH 114.2 Introduction to Sets, Logic and Algebra

MTH 114.2a Set Theory –with proofs of set theoretic theorems involving union, intersection, and compliments of sets.

Difference sets, De Morgan’s Laws, Power Sets; Poset Diagrams, Cardinality of a set. Product sets and relations on sets. Logic- statements and statement formula, connectives and truth tables. Implication and equivalence. Quantifiers and quantified statements. Truth functions. Substitution and replacements inn statements. Elementary notions of prepositional and predicate logic proofs. Rules of inference Techniques (direct, indirect, elimination and contradiction). Demonstration of proof.

MTH 114.2a Set Theory –with proofs of set theoretic theorems involving union, intersection, and compliments of sets.

Difference sets, De Morgan’s Laws, Power Sets; Poset Diagrams, Cardinality of a set. Product sets and relations on sets. Logic- statements and statement formula, connectives and truth tables. Implication and equivalence. Quantifiers and quantified statements. Truth functions. Substitution and replacements inn statements. Elementary notions of prepositional and predicate logic proofs. Rules of inference Techniques (direct, indirect, elimination and contradiction). Demonstration of proof.

MTH 210.1 Linear Algebra

Vectors space over the real field. Subspaces, linear independence, basis and dimension. Linear transformations and their representation by matrix – range, null space, rank. Singular and non-singular transformation and matrices. Systems linear equation and change of basis, equivalence and similarity. Eigenvalues and Eigenvectors. Minimum and characteristic polynomials linear transformation (Matrix).

Caley-Hamilton Theorem. Bilinear and quadratic.

Vectors space over the real field. Subspaces, linear independence, basis and dimension. Linear transformations and their representation by matrix – range, null space, rank. Singular and non-singular transformation and matrices. Systems linear equation and change of basis, equivalence and similarity. Eigenvalues and Eigenvectors. Minimum and characteristic polynomials linear transformation (Matrix).

Caley-Hamilton Theorem. Bilinear and quadratic.

MTH 220.1 Introduction to Real Analysis

Real numbers: order – upper and lower bounds. Least upper bounds axiom for real numbers and its consequences. Basic properties of convergent sequences. Upper and lower limits. Monotonic sequences. Cauchy’s principles of convergence. Series (of positive terms): Integral test. Euler’s constant. Index and ration tests. Comparison test for series. Alternating series tests for series. Series in General Absolute and conditional convergence. Atel and Dirichet test. Rearrangement properties. Power series – Circle of convergence and multiplication series. Function of a Real variables: Continuity of a set. Elementary properties of continuous functions, uniform continuity. Monotonic functions. Differentiation of functions of a real variable: Mean value theorem Rolle’s Theorem. etc. and its applications. De L’Hospital’s theorem. Tailors series with remainder. Maxima and minima.

Real numbers: order – upper and lower bounds. Least upper bounds axiom for real numbers and its consequences. Basic properties of convergent sequences. Upper and lower limits. Monotonic sequences. Cauchy’s principles of convergence. Series (of positive terms): Integral test. Euler’s constant. Index and ration tests. Comparison test for series. Alternating series tests for series. Series in General Absolute and conditional convergence. Atel and Dirichet test. Rearrangement properties. Power series – Circle of convergence and multiplication series. Function of a Real variables: Continuity of a set. Elementary properties of continuous functions, uniform continuity. Monotonic functions. Differentiation of functions of a real variable: Mean value theorem Rolle’s Theorem. etc. and its applications. De L’Hospital’s theorem. Tailors series with remainder. Maxima and minima.

MTH 230.1 Modern Algebra

Review of mappings relations, permutations, equivalence relations on a set. Review of integers- divisibility, division algorithm congruence modulo and Diophantine equation. Binary operations, algebraic structures-groups, semigroups, rings groups with examples, Groups and subgroups. Cossets in groups. Legranges theorem and applications. Cyclic subgroups and cyclic groups. Normal subgroups. Homomorphism of groups quotient groups. Isomorphism of groups. Concrete examples of groups. Groups of orders 2 to 8 including permutation group S and dinedrol groups D4. Partially orders set diagram of sub-groups.

Review of mappings relations, permutations, equivalence relations on a set. Review of integers- divisibility, division algorithm congruence modulo and Diophantine equation. Binary operations, algebraic structures-groups, semigroups, rings groups with examples, Groups and subgroups. Cossets in groups. Legranges theorem and applications. Cyclic subgroups and cyclic groups. Normal subgroups. Homomorphism of groups quotient groups. Isomorphism of groups. Concrete examples of groups. Groups of orders 2 to 8 including permutation group S and dinedrol groups D4. Partially orders set diagram of sub-groups.

STA 260.1 Introduction to Probability and Statistics

Definition of probability, frequency and probability of events. Equally likely events counting techniques. Conditional probability. (Baye’s Theorem) independent events, random variables, probability distributions. The central limit theorem, mathematical expectation, moments, the mean, variance, variance of a sum, covariance and correlation, conditional expectation.

Analysis of variance plus contingency tables plus parametric inference.

Definition of probability, frequency and probability of events. Equally likely events counting techniques. Conditional probability. (Baye’s Theorem) independent events, random variables, probability distributions. The central limit theorem, mathematical expectation, moments, the mean, variance, variance of a sum, covariance and correlation, conditional expectation.

Analysis of variance plus contingency tables plus parametric inference.

STA 261.1 Statistical Inference I

Sampling and sampling distribution. Point and interval Estimation. Principles of hypotheses testing. Test of hypotheses concerning population means, proportions and variances of large and small samples, and small sample cases. Goodness –fit tests. Analysis of variance.

Sampling and sampling distribution. Point and interval Estimation. Principles of hypotheses testing. Test of hypotheses concerning population means, proportions and variances of large and small samples, and small sample cases. Goodness –fit tests. Analysis of variance.

MTH 264.1 Statistics for Agric. And Biological Sciences

Use of Statistical methods in biology and agriculture. Frequency distribution. Laws of probability. The binomial. Poisson and normal probability distributions. Estimation and test of hypothesis. The binomial design of simple agricultural and biological experiments. analysis of variance and covariance, simple regression and correlations, contingency tables. Some non-parametric test. (This course is not for Students in the Department of Mathematics and Statistics.)

Use of Statistical methods in biology and agriculture. Frequency distribution. Laws of probability. The binomial. Poisson and normal probability distributions. Estimation and test of hypothesis. The binomial design of simple agricultural and biological experiments. analysis of variance and covariance, simple regression and correlations, contingency tables. Some non-parametric test. (This course is not for Students in the Department of Mathematics and Statistics.)

MTH 270.1 Introduction to Numerical Analysis

Solution of algebraic and transcendental equations. Curve fitting. Error analysis. Interpolation and approximation. Zeros or non-linear equation to one variable Systems of linear equations. Numerical differentiation and integral equation. Initial value problems for ordinary differential equation.

Solution of algebraic and transcendental equations. Curve fitting. Error analysis. Interpolation and approximation. Zeros or non-linear equation to one variable Systems of linear equations. Numerical differentiation and integral equation. Initial value problems for ordinary differential equation.

CSC 280.1 Introduction to Computer Programming

Principles of programming. Program design, algorithms, flowcharts, Pseudocodes. Programming with FORTRAN: declarations, input/output, loops, decisions, arithmetic/assignment statements. Arrays and subroutines.

Principles of programming. Program design, algorithms, flowcharts, Pseudocodes. Programming with FORTRAN: declarations, input/output, loops, decisions, arithmetic/assignment statements. Arrays and subroutines.

CSC 288.1 Structured Programming

Principles of good programming style, expression; structured programming concepts; control flow-invariant relation of a loop; stepwise refinement of both statement and data; program modularization (Bottom up approach, to-down approach, nested virtual machine approach); languages for structured programming debugging testing verifying code inspection; semantic analysis. Test construction. Program verification, test generation and running. The use of PASCAL to illustrate these concepts. String processing, Record Structures, file Processing, Dynamic data types for lists, etc. Recursion for tree search, sorting, etc. writing efficient programs. Turbo PASCAL project management facilities.

Principles of good programming style, expression; structured programming concepts; control flow-invariant relation of a loop; stepwise refinement of both statement and data; program modularization (Bottom up approach, to-down approach, nested virtual machine approach); languages for structured programming debugging testing verifying code inspection; semantic analysis. Test construction. Program verification, test generation and running. The use of PASCAL to illustrate these concepts. String processing, Record Structures, file Processing, Dynamic data types for lists, etc. Recursion for tree search, sorting, etc. writing efficient programs. Turbo PASCAL project management facilities.

CSC 283.1 Introduction to Information Systems and File Structures (2 Units)

Data hierarchy: bits bytes, data types, records, files. File design: serial and sequential files, random and index sequential files. File maintenance: master files, transaction files, etc. Tape and disk devices: timing, record blocking, etc.

Data hierarchy: bits bytes, data types, records, files. File design: serial and sequential files, random and index sequential files. File maintenance: master files, transaction files, etc. Tape and disk devices: timing, record blocking, etc.

MTH 290.2 Mathematics and Statistical Computing I

Introduction to MATLAB, Numerical and Symbolic calculations, Solving polynomial equations Solution of system of linear equations, Basic plotting and Graphs, Limits of functions, Differentiation, Integration, Data analysis and curve fitting, Numerical differentiation and integration. Probability of events. Conditional probability (Baye’s Theorem). Independent Events. Probability Distributions. Expectation and Conditional Expectation. Moments, the Mean, Variance of a Random Variables, Regression, Covariance and Correlation, Parametric Test and Non-Parametric Test.

Analysis of variance (One-way ANOVA and Two-way ANOVA with/without INTERACTION) plus Contingency tables plus parametric inference. Tests of Independence: Two-way or more (Contingency) Table

Parametric Test for One and Two Independent and dependent Samples: one sample test, two samples test (Construction of Confidence Intervals between Means, Hypothesis Testing about the Means and Variance) e.g. t-test, Z-test and F-test.

Non-Parametric Test for One, Two or more Independent Samples: Runs Test, Sign Test, Kolmogorov-Smirnov Test, Wilcoxon Signed Rank test and Mann Whitney U test, Kruskal-wallis test, non-parametric Levene test and Fligher Killean test.

Introduction to MATLAB, Numerical and Symbolic calculations, Solving polynomial equations Solution of system of linear equations, Basic plotting and Graphs, Limits of functions, Differentiation, Integration, Data analysis and curve fitting, Numerical differentiation and integration. Probability of events. Conditional probability (Baye’s Theorem). Independent Events. Probability Distributions. Expectation and Conditional Expectation. Moments, the Mean, Variance of a Random Variables, Regression, Covariance and Correlation, Parametric Test and Non-Parametric Test.

Analysis of variance (One-way ANOVA and Two-way ANOVA with/without INTERACTION) plus Contingency tables plus parametric inference. Tests of Independence: Two-way or more (Contingency) Table

Parametric Test for One and Two Independent and dependent Samples: one sample test, two samples test (Construction of Confidence Intervals between Means, Hypothesis Testing about the Means and Variance) e.g. t-test, Z-test and F-test.

Non-Parametric Test for One, Two or more Independent Samples: Runs Test, Sign Test, Kolmogorov-Smirnov Test, Wilcoxon Signed Rank test and Mann Whitney U test, Kruskal-wallis test, non-parametric Levene test and Fligher Killean test.

MTH 224.2 Mathematical Methods I

Review of differentiation and integration and their applications and mean value theorem. Taylor series. Real –valued functions or two or three variables. Partial derivatives chain rule, extreme Lagrange multipliers. Increments, differentials and linear approximations. Evaluation of line, integrals, multiple integrals. Integrals transform and applications

Review of differentiation and integration and their applications and mean value theorem. Taylor series. Real –valued functions or two or three variables. Partial derivatives chain rule, extreme Lagrange multipliers. Increments, differentials and linear approximations. Evaluation of line, integrals, multiple integrals. Integrals transform and applications

MTH 226.2 Real Analysis II

Metric spaces: Metrics, Norms. Examples of metric spaces. Minikowski’s inequality. Open balls, closed balls, spheres. Open sets, closed sets. Closure of a set. Foundary and diametric subspaces of a metric space. Continuous functions on metric spaces. Complete metric spaces. Subsets of complete metric spaces. Complete metric spaces. Subsets of complete metric space. Completion of compact spaces. Finite intersection property. The Heine-Borel Theorem.

Integration: The Riemann-Stieljes integral of bounded functions. Conditions of integrality. Properties of Riemann integrals. Fundamental theorem of integration. Mean value theorems of integrals. Integration by parts and by substitution.

Metric spaces: Metrics, Norms. Examples of metric spaces. Minikowski’s inequality. Open balls, closed balls, spheres. Open sets, closed sets. Closure of a set. Foundary and diametric subspaces of a metric space. Continuous functions on metric spaces. Complete metric spaces. Subsets of complete metric spaces. Complete metric spaces. Subsets of complete metric space. Completion of compact spaces. Finite intersection property. The Heine-Borel Theorem.

Integration: The Riemann-Stieljes integral of bounded functions. Conditions of integrality. Properties of Riemann integrals. Fundamental theorem of integration. Mean value theorems of integrals. Integration by parts and by substitution.

MTH 240.2 Vector Analysis

Review of vectors. Equation of curves and surfaces. Vector differentiation and applications. Gradient, divergence and curl. Vectors integrals, line, surface and volume integrals. Green’s, Stoke’ and divergence theorems. Applications. Tensor products of vector spaces. Tensor algebra. Symmetry. Cartesian tensors.

Review of vectors. Equation of curves and surfaces. Vector differentiation and applications. Gradient, divergence and curl. Vectors integrals, line, surface and volume integrals. Green’s, Stoke’ and divergence theorems. Applications. Tensor products of vector spaces. Tensor algebra. Symmetry. Cartesian tensors.

MTH 250.2 Elementary Differential Equations

First order ordinary differential equations. Existence and uniqueness. Second order ordinary differential equations with constant co-efficient. General theory of nth order linear equations. Laplace transform solution of initial-value problem by Laplace transform method. Sturm Liurville problems and applications. Simple treatment of partial differential equations in two independent variables. Application of O.D.E to physical, life and social sciences. Pre-requisite MTH120.1.

First order ordinary differential equations. Existence and uniqueness. Second order ordinary differential equations with constant co-efficient. General theory of nth order linear equations. Laplace transform solution of initial-value problem by Laplace transform method. Sturm Liurville problems and applications. Simple treatment of partial differential equations in two independent variables. Application of O.D.E to physical, life and social sciences. Pre-requisite MTH120.1.

STA 262.2 Mathematical Statistics I

Distribution of random variables, the probability density function, the distribution function, the moment generating function, characteristic functions, factorial moments, Chebyshev’s inequality. Conditional probability and stochastic independence marginal and conditional distributions, the correlation coefficient covariance.

Distributions of functions of random variables, sampling theory, transformation of variables of the discrete and continuous types, the t and F distributions, the moment generating function technique.

Distribution of random variables, the probability density function, the distribution function, the moment generating function, characteristic functions, factorial moments, Chebyshev’s inequality. Conditional probability and stochastic independence marginal and conditional distributions, the correlation coefficient covariance.

Distributions of functions of random variables, sampling theory, transformation of variables of the discrete and continuous types, the t and F distributions, the moment generating function technique.

CSC 282.2 Database Programming

Characteristics of business programming. Records, files. File creation, accessing. Record accessing, insertion, updating, deletion. Searching and retrievals. Programming with dBase, and MS Access, or other suitable language. Introduction to SQL.

Characteristics of business programming. Records, files. File creation, accessing. Record accessing, insertion, updating, deletion. Searching and retrievals. Programming with dBase, and MS Access, or other suitable language. Introduction to SQL.

CSC 286.2 Data Structures

Bits, Bytes, words, linear structures and lists structures; arrays, tree structures, sets and relations, higher level language data types and data-handling facilities. Techniques for storing structured data list, files, tables trees, etc., their space and access time properties, algorithm for manipulating linked lists, binary, b-trees, b*trees, and A VIAL trees. Algorithm for transversing and balancing trees.

Bits, Bytes, words, linear structures and lists structures; arrays, tree structures, sets and relations, higher level language data types and data-handling facilities. Techniques for storing structured data list, files, tables trees, etc., their space and access time properties, algorithm for manipulating linked lists, binary, b-trees, b*trees, and A VIAL trees. Algorithm for transversing and balancing trees.

CSC 287.2 Object Oriented ProgrammingI

Preprocessor directives, library naming and access, comments, statements. Data types, constants, variables, expressions and assignment statements. String class. Input/output statements. Selection, repetition. Functions. Arrays. File manipulation, Pointers, and Classes. Use C language, C++ or C# to illustrate these concepts.

FSC 2C1.2 Community Service

The course is geared towards community development with the aim of creating a positive influence to the immediate environment and host community.

The course is geared towards community development with the aim of creating a positive influence to the immediate environment and host community.

B.Sc. MATHEMATICS COURSES YEAR III

MTH 390.1 MATHEMATICAL COMPUTING II

Plotting of second order solution family of differential equations, plotting of third order solution family of differential equations, plotting of recursive sequences, study the convergence of sequences through plotting, verify Bolzano Weierstrass theorem through plotting of sequences and hence identify convergence subsequent from the plot, Cauchy ratio test by plotting the roots, ratio test by plotting the ratio of nth and (n +1)th term, Laplace and Fourier transform.

Plotting of second order solution family of differential equations, plotting of third order solution family of differential equations, plotting of recursive sequences, study the convergence of sequences through plotting, verify Bolzano Weierstrass theorem through plotting of sequences and hence identify convergence subsequent from the plot, Cauchy ratio test by plotting the roots, ratio test by plotting the ratio of nth and (n +1)th term, Laplace and Fourier transform.

MTH 310.1 Modern Algebra II

Rings, integral domains, division rings, field rings of polynomials, and matrices, quaternious rings. Homomorphism theorem for rings. Quotient rings. Ideals Polynomial rings and factorization-Euclidean algorithm and god for rings. Fundamental theorem of algebra.

Rings, integral domains, division rings, field rings of polynomials, and matrices, quaternious rings. Homomorphism theorem for rings. Quotient rings. Ideals Polynomial rings and factorization-Euclidean algorithm and god for rings. Fundamental theorem of algebra.

MTH 320.1 Real Analysis III

Integration: Review of Riemann-Stieljes integrals. Improper Riemann-Stieljes integrals. Functions of Bounded variations, Sequences and Series of Function, Sequences in metric spaces. Cluster points of a sequence, Cauchy sequence, Sequences and series of functions. Uniform convergence of sequences and of functions. Test for uniform convergence of series, and properties of uniformly convergent series power series. Weiestrass approximation theorem.

Integration: Review of Riemann-Stieljes integrals. Improper Riemann-Stieljes integrals. Functions of Bounded variations, Sequences and Series of Function, Sequences in metric spaces. Cluster points of a sequence, Cauchy sequence, Sequences and series of functions. Uniform convergence of sequences and of functions. Test for uniform convergence of series, and properties of uniformly convergent series power series. Weiestrass approximation theorem.

Function of several Variables: The n-dimensional Euclidean space. Continuity, Partial and total derivatives. Chain rule. Implicit functions theorem. The inverse function theorem. Directional derivatives. Higher partial derivatives. The mean value theorems. Taylor series. Maxima and minima of function of several variables. Necessary conditions for free and constrained cases. Lagrange multi-pliers. Integration of Functions of Several Variables. Definition of multiple integrals as limit of sum. Evaluation of multiple integrals (transformation of integrals). Line integrals and Green’s formula. Uniform Convergence: Uniformly convergent sequences and series of analytic functions and their properties. Infinite products. Absolute and uniform convergence of infinite products.

MTH 324.1 Complex Analysis I

Functions of a complex variable. Limits and continuity of functions of complex variable. Deriving the Cauchy-Riemann equations. Analytic functions. Bilinear transformations, conformal mapping contour integrals. Cauchy’s theorems and consequences. Convergence of sequences and series of functions of complex variable. Power series. Taylor series. Laurent expansions. Isolated singularities and residues.

Functions of a complex variable. Limits and continuity of functions of complex variable. Deriving the Cauchy-Riemann equations. Analytic functions. Bilinear transformations, conformal mapping contour integrals. Cauchy’s theorems and consequences. Convergence of sequences and series of functions of complex variable. Power series. Taylor series. Laurent expansions. Isolated singularities and residues.

MTH 330.1 Topology

Review of metric spaces. Dence subsets of metric space. Compactness connectedness of metric space. Topological spaces, definition, open and closed sets, neighbourhoods, Coarser and finer topologies. Basis and sub-bases. Separation axioms, Compactness, local compactness, connectedness. Construction of new topological spaces from given homeomorphism, topological invariance, spaces of continuous function: point-wise and uniform convergence.

Review of metric spaces. Dence subsets of metric space. Compactness connectedness of metric space. Topological spaces, definition, open and closed sets, neighbourhoods, Coarser and finer topologies. Basis and sub-bases. Separation axioms, Compactness, local compactness, connectedness. Construction of new topological spaces from given homeomorphism, topological invariance, spaces of continuous function: point-wise and uniform convergence.

MTH 340.1 Ordinary Differential Equations I

Series solution of second order linear equations. Bossel, Legendre and hypergeometric equations and functions gamma Beta functions sturnliovelle problems. Orthogonal polynomials and functions, fourier, Fomier-Bessel and Fmier Legendre series. Fourie transformation. Solution of laplace, wave ad heat equations by Fourier method.

Series solution of second order linear equations. Bossel, Legendre and hypergeometric equations and functions gamma Beta functions sturnliovelle problems. Orthogonal polynomials and functions, fourier, Fomier-Bessel and Fmier Legendre series. Fourie transformation. Solution of laplace, wave ad heat equations by Fourier method.

MTH 350.1 Rigid Body Dynamics

General motion of a rigid body and a translation plus a rotation. Moment. And products of inertia in three dimension. Parallel and perpendicular axes theorems. Principles axes, Angular momentum, kinetic energy of a rigid body. Impulsive motion. Examples involving one and two dimensional motion of simple systems. Moving frames of reference rotating and translating frames of reference. Coriolis force. Motion near the Earth’s surface. The Foucault’s pendulum. Euler’s dynamical equations for motion of a rigid body with one point fixed the symmetrical top.

General motion of a rigid body and a translation plus a rotation. Moment. And products of inertia in three dimension. Parallel and perpendicular axes theorems. Principles axes, Angular momentum, kinetic energy of a rigid body. Impulsive motion. Examples involving one and two dimensional motion of simple systems. Moving frames of reference rotating and translating frames of reference. Coriolis force. Motion near the Earth’s surface. The Foucault’s pendulum. Euler’s dynamical equations for motion of a rigid body with one point fixed the symmetrical top.

MTH 312.1 Discrete and Combinatorial Mathematics

Groups and subgroups, group axioms, Permutation groups, cosets, Generation of groups and defining relations. Graphs, directed and undirected graphs, subgraphs, cycles, connectivity, application (flow charts) and state transition graphs-lattices and Eollean algebra, finite fields, minipolynomials. Irreducible polynomials, polynominal roots application (error-correcting codes, sequences generators) coding theory. Introduction to combinatorics.

Groups and subgroups, group axioms, Permutation groups, cosets, Generation of groups and defining relations. Graphs, directed and undirected graphs, subgraphs, cycles, connectivity, application (flow charts) and state transition graphs-lattices and Eollean algebra, finite fields, minipolynomials. Irreducible polynomials, polynominal roots application (error-correcting codes, sequences generators) coding theory. Introduction to combinatorics.

STA 360.1 Mathematical Statistics II

Distribution: Bivariate normal distribution, the gamma, chi-square, 2 types of beta distribution of functions of random variables. Probability integral transformation. Bivariate moment generating functions, univariate characteristic functions. Various modes of convergence, laws of large numbers and the central limit theorem using characteristic function.

Distribution: Bivariate normal distribution, the gamma, chi-square, 2 types of beta distribution of functions of random variables. Probability integral transformation. Bivariate moment generating functions, univariate characteristic functions. Various modes of convergence, laws of large numbers and the central limit theorem using characteristic function.

STA 370.1 Operations Research

Definition and scope of operations research. Elementary inventory models, replacement maintenance and reliability problem. Linear programming: formulations and simplex method. Allocation problems (simplex, assignment and transportation algorithms) and their applications to routing problems. Queueing theory, Game theory, sequencing problems.

Definition and scope of operations research. Elementary inventory models, replacement maintenance and reliability problem. Linear programming: formulations and simplex method. Allocation problems (simplex, assignment and transportation algorithms) and their applications to routing problems. Queueing theory, Game theory, sequencing problems.

STA 362.1 Statistical Inference II

Estimation with normal models. Point estimation, by least square, and maximum likelihood methods. Properties of point estimators; unbiasedness sufficiency, completeness, uniformly minimum variance unbiasedness. Cramer-Rao inequality, consistence, efficiency, best asymptotic normality. Interval estimaties; esatimation of mean and variance, comparison of two means and two variances; estimation involving pair observations. General methods of finding confidence bound.

Test of hypothesis: types of errors, power function, one tailed and two tailed tests, other chi-squared test and contingency test. Likelihood ratio. Nyman-Pearson theorem.

Estimation with normal models. Point estimation, by least square, and maximum likelihood methods. Properties of point estimators; unbiasedness sufficiency, completeness, uniformly minimum variance unbiasedness. Cramer-Rao inequality, consistence, efficiency, best asymptotic normality. Interval estimaties; esatimation of mean and variance, comparison of two means and two variances; estimation involving pair observations. General methods of finding confidence bound.

Test of hypothesis: types of errors, power function, one tailed and two tailed tests, other chi-squared test and contingency test. Likelihood ratio. Nyman-Pearson theorem.

STA 372.1 Quality Control

Fundamentals of survey sampling; survey and sampling designs, mechanical selection, randomization and frames. Review of sampling techniques; simple random sampling, stratified, cluster, quota and systematic sampling. Sub-sampling and multi-stage sampling. Statistical analysis of the sampling methods.

Fundamentals of survey sampling; survey and sampling designs, mechanical selection, randomization and frames. Review of sampling techniques; simple random sampling, stratified, cluster, quota and systematic sampling. Sub-sampling and multi-stage sampling. Statistical analysis of the sampling methods.

STA 363.2 Distribution Theory

Bivariate normal distribution, the gamma, chi-squared, beta I2types), t and f, distribution. Distribution of functions of random variables: Cumulative distribution function, Moment generating function Transformation (change of variable) techniques. Distribution of order statistics.

Bivariate normal distribution, the gamma, chi-squared, beta I2types), t and f, distribution. Distribution of functions of random variables: Cumulative distribution function, Moment generating function Transformation (change of variable) techniques. Distribution of order statistics.

CSC 397.1 Computational Methods

Computational Geometry-convex hull, triangulation, curves and surfacing. Formal specification, Bunches and bunch theory, pigeonhole principles, surjection, injections, inverses, composition, reflexivity, equivalence relations, transitivity, cardinality – relate practical examples to appropriate termination detection. Implications of uncomputability, tractable and intractable problems. Optical computing – integrity models such as Biba and Clark – Wilson.

CSC 394.1 Operating Systems

Principles of operating systems; Types of operating systems, batch, multi- programming multiprocessing. Processes, inter processor communication, synchronization, deadlocks storage management and resource allocation. illustrated from a popular operating system such as UNIX.

CSC 382.1 Computer Architecture 1

Basic logic design and Circuits; Data representation; instruction formats; computer Architecture; Study architecture of an actual simple mini-computer. Assembly languages and assemblers-the two-stage operation of the assembler. Machine instruction sets. Bootstrap Programs and Link Editors.

CSC 396.1 Automata theory, Computability and Formal Languages

The role of programming language. Benefits of high level language. Programming paradigms: imperative, Logic, functional and object-oriented programming. General/multi purpose programming languages. Language design and language evaluation criteria. Program structures and representations. Types, objects and declarations. Expressions and statements. Subprograms. Data structures. Input/output. Introductory notions in formal languages. Relationship to programming Languages. Issues in programming.

Basic logic design and Circuits; Data representation; instruction formats; computer Architecture; Study architecture of an actual simple mini-computer. Assembly languages and assemblers-the two-stage operation of the assembler. Machine instruction sets. Bootstrap Programs and Link Editors.

CSC 396.1 Automata theory, Computability and Formal Languages

The role of programming language. Benefits of high level language. Programming paradigms: imperative, Logic, functional and object-oriented programming. General/multi purpose programming languages. Language design and language evaluation criteria. Program structures and representations. Types, objects and declarations. Expressions and statements. Subprograms. Data structures. Input/output. Introductory notions in formal languages. Relationship to programming Languages. Issues in programming.

GES 300.1 Fundamentals of Entrepreneurship Development

History and the development of entrepreneurship, the entrepreneur Qualities and Characteristic; the entrepreneur and business environment; identify business opportunity; starting and developing new business ventures; Legal forms business ownership and Registration. Types of business Ownership; Feasibility Studies; Role of Small and Medium Scale Enterprise (SME) in the Economy; Role of government on Entrepreneurship; Business Location and Layout; Accounting for SME: Financing SME; Managing SME: Marketing in SME; risk Management of SME; Success and Failure factor of SME; Prospects and Challenges of Entrepreneurship; Ethical Behaviour in Small Business.

History and the development of entrepreneurship, the entrepreneur Qualities and Characteristic; the entrepreneur and business environment; identify business opportunity; starting and developing new business ventures; Legal forms business ownership and Registration. Types of business Ownership; Feasibility Studies; Role of Small and Medium Scale Enterprise (SME) in the Economy; Role of government on Entrepreneurship; Business Location and Layout; Accounting for SME: Financing SME; Managing SME: Marketing in SME; risk Management of SME; Success and Failure factor of SME; Prospects and Challenges of Entrepreneurship; Ethical Behaviour in Small Business.

STA 390.1 Statistical Computing II

General principles. Summary and inspection of data using tables and graphical methods. Sorting and ranking. Simulation. Algorithms for generation of uniform distribution in a given interval. Generation of random samples from non-uniform distribution such as exponential, normal, binomial distributions. Simple Data manipulation and use of files using a high level programming language, significance tests and confidence intervals.

Regression and ANOVA: computational techniques for fitting a given regression. Solution normal equations for full rank and less then full rank cases-Algorithm for solving triangular system of equations. e.g. Caussian elimination. Choleshy LU decomposition & variants of it, Householder transformations. Pre-requisite MTH260.1, MTH 262.2. Weighted least square: Algorithms for solving the normal equation. A generalized inverse of X’X using e.g.Choleshy method or Householder transformations. Orthogonal decomposition with identificability constraints. Singular value decomposition and applications. Centering and Scaling the data: Regression updating. Calculation of F statistics for a general linear hypothesis. Some method for checking on the accuracy of a given least square program. Working experience in the use of Pre-requisite MTH360.1

General principles. Summary and inspection of data using tables and graphical methods. Sorting and ranking. Simulation. Algorithms for generation of uniform distribution in a given interval. Generation of random samples from non-uniform distribution such as exponential, normal, binomial distributions. Simple Data manipulation and use of files using a high level programming language, significance tests and confidence intervals.

Regression and ANOVA: computational techniques for fitting a given regression. Solution normal equations for full rank and less then full rank cases-Algorithm for solving triangular system of equations. e.g. Caussian elimination. Choleshy LU decomposition & variants of it, Householder transformations. Pre-requisite MTH260.1, MTH 262.2. Weighted least square: Algorithms for solving the normal equation. A generalized inverse of X’X using e.g.Choleshy method or Householder transformations. Orthogonal decomposition with identificability constraints. Singular value decomposition and applications. Centering and Scaling the data: Regression updating. Calculation of F statistics for a general linear hypothesis. Some method for checking on the accuracy of a given least square program. Working experience in the use of Pre-requisite MTH360.1

STA 374.1 Probability I

Expectations (Moments) and Moment generating functions. Chabychev’s Inequality. Bivariate, marginal and conditional distributions and their moments. Convolution of two distributions.

STA 376.1 Statistical Quality Control

Process Control: Construction and uses of Control Charts (x, b and range). Tolerance limits Product control: Design of Sampling Plans (simple, double, multiple and sequential). Comparison of different sampling plans, Cusum, Mcusum etc.

MTH 352.1 Analytical Dynamics

Degrees of freedom. Holonomic and holonomic constraints Generalised co-ordinates Lagrange’s equations for holonomic system’s face dependent on co-ordinates only, force obtainable from a potential. Impulsive force

Degrees of freedom. Holonomic and holonomic constraints Generalised co-ordinates Lagrange’s equations for holonomic system’s face dependent on co-ordinates only, force obtainable from a potential. Impulsive force

STA 356.1 Demography

Definition of Basic concepts. Sources and assessment of Demographic data. Construction and uses of life tables. Estimation of Population parameters (also from defective data). Stable and Quasi-stable population. Models for population projections (examples from Nigerian Population.)

Definition of Basic concepts. Sources and assessment of Demographic data. Construction and uses of life tables. Estimation of Population parameters (also from defective data). Stable and Quasi-stable population. Models for population projections (examples from Nigerian Population.)

MTH 300.2 Industrial Training

The course is expected to give students an opportunity in public and private institutions/establishments during the second semester and long vacation to learn and gain knowledge on the basic and applied aspect of Mathematics. All students are attached to the organization for six months whereas those on probation are not eligible for the training.

The course is expected to give students an opportunity in public and private institutions/establishments during the second semester and long vacation to learn and gain knowledge on the basic and applied aspect of Mathematics. All students are attached to the organization for six months whereas those on probation are not eligible for the training.

B.Sc. MATHEMATICS COURSES YEAR IV

MTH 410.1 Group Theory

Abelian groups. Structure of finality generated abelian groups. Permutation representation of group actions. Burnside lemma; Sylow theorems. Derived groups. Nilpotent and soluble groups. Free groups. Groups of order 8 to 15.

Abelian groups. Structure of finality generated abelian groups. Permutation representation of group actions. Burnside lemma; Sylow theorems. Derived groups. Nilpotent and soluble groups. Free groups. Groups of order 8 to 15.

MTH 420.1 Functional Analysis

Contraction mapping theorem. Arzela-Ascoli lemma. Stone-Weierstrass theorem. Categories. Nowhere differentiable continuous functions.

Normedspaces: Banach spaces. Hahn-Banach theorem. Uniform boundedness principle. Open mapping and closed graph theorem. Riecz lemma. Duality theory in Banch spaces. Dual of LP spaces. Riecz representation theorm. Compact operators. The Riecz-Schauder theory.

Helbert spaces: Projection theorem. Riecz representation theorem.

Banch Algebras: Commutative Banach algegras. Maximal ideals Gelfard representation for Banach algebras with identity.

Contraction mapping theorem. Arzela-Ascoli lemma. Stone-Weierstrass theorem. Categories. Nowhere differentiable continuous functions.

Normedspaces: Banach spaces. Hahn-Banach theorem. Uniform boundedness principle. Open mapping and closed graph theorem. Riecz lemma. Duality theory in Banch spaces. Dual of LP spaces. Riecz representation theorm. Compact operators. The Riecz-Schauder theory.

Helbert spaces: Projection theorem. Riecz representation theorem.

Banch Algebras: Commutative Banach algegras. Maximal ideals Gelfard representation for Banach algebras with identity.

MTH 440.1 Partial Differential Equation

Linear equations of the first order, non-linear equations of the first order. Characteristics. Existence and uniquences of solutions. Second order linear and quasi-linear equations in two independent variables. Elliptic, hyperbolic and parabolic equations. Well set mathematical problems. Applications to equations of mathematical physics.

Linear equations of the first order, non-linear equations of the first order. Characteristics. Existence and uniquences of solutions. Second order linear and quasi-linear equations in two independent variables. Elliptic, hyperbolic and parabolic equations. Well set mathematical problems. Applications to equations of mathematical physics.

MTH 426.1 Complex Analysis II

Calculus of residue, and application to evaluation of integrals and to summation of series. Maximum modulus principle. Argument principle. Rouche’s theorem. The fundamental theorem of algebra. Principle of analytic continuation. Multiple valued functions and Riemann surfaces.

Calculus of residue, and application to evaluation of integrals and to summation of series. Maximum modulus principle. Argument principle. Rouche’s theorem. The fundamental theorem of algebra. Principle of analytic continuation. Multiple valued functions and Riemann surfaces.

MTH 442.1 Mathematical Methods II

Calculus of variation: Lagrange’s functional and associated density, Necessary condition for a weak relative extremum hamilton’s principles. Lagrange’s equations and geodesic problems. The Du Bois-Raymond equation and corner condition. Variable end-points and related theorms. Sufficient conditions for a minimum. Isoperimetric problems. Variational integral transforms. Laplace, Fourier and Hankel transforms. Complex variable methods convolution theorems. Application to solution of differential equations. Pre-requisite MTH 448.2

MTH 490.1 Mathematical Computing III

Solution to Cauchy problem for first order PDE, plotting characteristics for the first order PDE, plot the general integral surface of a given first order PDE with initial data, solution of wave equation, solution of one dimensional heat equation.

Approximate solution to initial problem using the following approximate methods, Euler method, modified Euler method, Rung-Kutta method, comparison between exact methods and approximate results for any representative differential equation

Solution to Cauchy problem for first order PDE, plotting characteristics for the first order PDE, plot the general integral surface of a given first order PDE with initial data, solution of wave equation, solution of one dimensional heat equation.

Approximate solution to initial problem using the following approximate methods, Euler method, modified Euler method, Rung-Kutta method, comparison between exact methods and approximate results for any representative differential equation

MTH 452.1 Quantum Mechanics

Dirac Formulation os Quantum Mechanics: linear spaces and operators, kets and bras. Hermitian operators; observables, eigen-functions, eigen-values, expectation values, probability omplitueds. Quantization conditions: poisson brackets and commutators; schrodinger representation in Cartesian coordinates. Upitary operators, corresponding to spatial translations and their infinitesimal generator, conservation of momentum. Schrodinger. And Heisenbery pictures. Heisenbery equations of motion. Creation and amitilation operators. Angular Momentum: Angular momentum operators as infinitesimal rotation generators (j) representation. Spin; Pauli matrices. Addition of angular moments with calculation of Clebach-Cordon coefficients. Wigher-theorem. Identical Particles and Spin: Physical meaning of identity. Symmetric and ant-symmetric wave function. Distinguishability of identical particles. The exclusion principles connection with statistical mechanics. Collision of identical particles. Spin and statistics. Hydrogen-like atom.

Dirac Formulation os Quantum Mechanics: linear spaces and operators, kets and bras. Hermitian operators; observables, eigen-functions, eigen-values, expectation values, probability omplitueds. Quantization conditions: poisson brackets and commutators; schrodinger representation in Cartesian coordinates. Upitary operators, corresponding to spatial translations and their infinitesimal generator, conservation of momentum. Schrodinger. And Heisenbery pictures. Heisenbery equations of motion. Creation and amitilation operators. Angular Momentum: Angular momentum operators as infinitesimal rotation generators (j) representation. Spin; Pauli matrices. Addition of angular moments with calculation of Clebach-Cordon coefficients. Wigher-theorem. Identical Particles and Spin: Physical meaning of identity. Symmetric and ant-symmetric wave function. Distinguishability of identical particles. The exclusion principles connection with statistical mechanics. Collision of identical particles. Spin and statistics. Hydrogen-like atom.

MTH 454.1 Fluid Mechanics

Cartesian tensors and the Navier Stokes equation; some exact solutions. Regnolds Number.

Invisid flow: The Eulers equation. Velocity potential and stream functions. Sources and sinks. Circulation and vorticity. Flow past a circular cylinder. Complex potential. Confermal transformation. Viscous flow: the boundary layer approximations in incompressible flow. Similar exact solutions. Approximate solutions. Heat transfer in boundary layer flows. Boundary layer theory. Free convection flows.

Cartesian tensors and the Navier Stokes equation; some exact solutions. Regnolds Number.

Invisid flow: The Eulers equation. Velocity potential and stream functions. Sources and sinks. Circulation and vorticity. Flow past a circular cylinder. Complex potential. Confermal transformation. Viscous flow: the boundary layer approximations in incompressible flow. Similar exact solutions. Approximate solutions. Heat transfer in boundary layer flows. Boundary layer theory. Free convection flows.

MTH 456.1 Elasticity

Analysis of Stress and strain: the stress vector and the stress tensor. The body stress equation. The displacement vector. Strain components. Stress and strain invariants. Transformation of stress and strain. Equations of compatibility of strain and equation of equilibrium. The Elastic Solid: The Lame’s stress-strain relations of isotropic elasticity. Young’s modulus and Poisson’s ratio. Strain energy function and derivation of general stress-strain relations. The fundamental partial differential wquatuion for the distortional vector. Velocities of dillational and distortional waves. The equations of elasticity in complex coordinates. Uniqueness of solution; Saint-Venant principles. Generalized Hooke’s law, anisotropy, isotopy and elastic constants. Two-Dimensional Elasticity: Plane strain and generalized plane stress by Airy stress function and complex potential method. Tension, torsion and flexure with sheer of beams and rods. Elementary theory of thin plates under trans-verse loads.

Three-Dimensional Elasticity: Simple three-dimensional solution of the fundamental equation: force-nucleus in infinite solid. Isolated force on Plane boundary of semi-infinite solid. Rigid sphere cemented into infinite elastic solid. Orthogonal curvilinear coordinates. Application to circular cylindrical shafts in steady motion; torsion of shafts or verying circular cross-section; live’s biharmonic stress function in problems of axial symmetry.

Analysis of Stress and strain: the stress vector and the stress tensor. The body stress equation. The displacement vector. Strain components. Stress and strain invariants. Transformation of stress and strain. Equations of compatibility of strain and equation of equilibrium. The Elastic Solid: The Lame’s stress-strain relations of isotropic elasticity. Young’s modulus and Poisson’s ratio. Strain energy function and derivation of general stress-strain relations. The fundamental partial differential wquatuion for the distortional vector. Velocities of dillational and distortional waves. The equations of elasticity in complex coordinates. Uniqueness of solution; Saint-Venant principles. Generalized Hooke’s law, anisotropy, isotopy and elastic constants. Two-Dimensional Elasticity: Plane strain and generalized plane stress by Airy stress function and complex potential method. Tension, torsion and flexure with sheer of beams and rods. Elementary theory of thin plates under trans-verse loads.

Three-Dimensional Elasticity: Simple three-dimensional solution of the fundamental equation: force-nucleus in infinite solid. Isolated force on Plane boundary of semi-infinite solid. Rigid sphere cemented into infinite elastic solid. Orthogonal curvilinear coordinates. Application to circular cylindrical shafts in steady motion; torsion of shafts or verying circular cross-section; live’s biharmonic stress function in problems of axial symmetry.

STA 466.1 Optimization Methods

Linear Programming: Revised Simplex methods, duality theory and applications. Unconstrained Optimization: Search methods, Grid, Nelder and Meads Methods. Gradient methods for unconstrained optimization; steepest descent, Newton-Raphson, constrained: classical methods of optimization, Maxima and Minima, Lagrange’s multipliers. Kuhn-Tucker conditions. Parametric programming, integer programming. Dynamic programming. Pre-requisite MTH 370.1.

Linear Programming: Revised Simplex methods, duality theory and applications. Unconstrained Optimization: Search methods, Grid, Nelder and Meads Methods. Gradient methods for unconstrained optimization; steepest descent, Newton-Raphson, constrained: classical methods of optimization, Maxima and Minima, Lagrange’s multipliers. Kuhn-Tucker conditions. Parametric programming, integer programming. Dynamic programming. Pre-requisite MTH 370.1.

MTH 444.1 Mathematical Modeling

Modeling with differential and integral equations; The logistic curve Problem of growth and decay. Solution of problem of growth of two conflicting populations physical models-sterring, rocket and flow problems. Differentive models. Chemical Models. Mathematical modeling of intramuscular injection. The problem of the pendulum and introduction to elliptic integrals. Radiative test transfer and solution of integral equations. Stochastic modules and applications to games theory-network flow problems.

Modeling with differential and integral equations; The logistic curve Problem of growth and decay. Solution of problem of growth of two conflicting populations physical models-sterring, rocket and flow problems. Differentive models. Chemical Models. Mathematical modeling of intramuscular injection. The problem of the pendulum and introduction to elliptic integrals. Radiative test transfer and solution of integral equations. Stochastic modules and applications to games theory-network flow problems.

MTH 413.1 Number Theory

Residue classes, the Fermat-Euler theorem. Solution of congruence of a prime modulus. Primitive roots Arithmetic functions, multiplicative functions. The function (n), u(n), d(n), o(n), r(n). Orders of magnitude of these functions. The representation f numbers as sums of squares. Some simple Diophantine equations. Rationals and irrationals. The distribution of prime numbers. The work of Tchebycheff, Hertens and Riemann, The Riemann Zeta-function. The prime theorem with de la Vallee Poussin’s form of the error term. Dirichlet characters and series primes in arithmetic progression.

Residue classes, the Fermat-Euler theorem. Solution of congruence of a prime modulus. Primitive roots Arithmetic functions, multiplicative functions. The function (n), u(n), d(n), o(n), r(n). Orders of magnitude of these functions. The representation f numbers as sums of squares. Some simple Diophantine equations. Rationals and irrationals. The distribution of prime numbers. The work of Tchebycheff, Hertens and Riemann, The Riemann Zeta-function. The prime theorem with de la Vallee Poussin’s form of the error term. Dirichlet characters and series primes in arithmetic progression.

CSC481.1 Object-Oriented Programming II

Object-Oriented programming structures and principles. Practical illustration with Java, Rubby, and Python programming languages. Preprocessor directives, library naming and access, comments, statements. Data types, constants, variables, expressions and assignment statements. String class. Input/output statements. Selection, repetition. Functions. arrays. Files manipulation. Classes and object-oriented design.

Object-Oriented programming structures and principles. Practical illustration with Java, Rubby, and Python programming languages. Preprocessor directives, library naming and access, comments, statements. Data types, constants, variables, expressions and assignment statements. String class. Input/output statements. Selection, repetition. Functions. arrays. Files manipulation. Classes and object-oriented design.

STA 490.1 Statistical Computing III

Estimation of mean vector and the covariance matrix. Using The distribution and used of sample correlation coefficient. The generalized T2- statistics. Principal components and factor analysis. Multiple linear regression models, polynomial regresson. Tests of independence and goodness-of- fit

Estimation of mean vector and the covariance matrix. Using The distribution and used of sample correlation coefficient. The generalized T2- statistics. Principal components and factor analysis. Multiple linear regression models, polynomial regresson. Tests of independence and goodness-of- fit

STA 462.1 Design and analysis of Experiments

Basic design, completely random, randomized block and Latin square designs. Use of models for estimating effects; missing data and confidence limits. Graeco Latin square and split plot designs. Analysis is variance and hypotheses tests. Factorial experiments, the 22 and 23 experiments, standard errors for factorial effects. Confounding factorials in blocks, fractional factorials factors at 2 levels and 3 levels. In complete block designs, estimation of model parameters analysis of variance of BIB experiments (with symmetrical BIB arrangement). Pre-requisite MTH 360.1.

Basic design, completely random, randomized block and Latin square designs. Use of models for estimating effects; missing data and confidence limits. Graeco Latin square and split plot designs. Analysis is variance and hypotheses tests. Factorial experiments, the 22 and 23 experiments, standard errors for factorial effects. Confounding factorials in blocks, fractional factorials factors at 2 levels and 3 levels. In complete block designs, estimation of model parameters analysis of variance of BIB experiments (with symmetrical BIB arrangement). Pre-requisite MTH 360.1.

STA 463.1 Multivariate Analysis

The multivariate normal distribution. Estimation of mean vector and the covariance matrix. The distribution and used of sample correlation coefficient. The generalized T2- statistics. Classification of observations. Procedures of classification into one of two or three specified multicariate normal populations. Discriminant function when populations are unknown. Principal components and factor analysis

The multivariate normal distribution. Estimation of mean vector and the covariance matrix. The distribution and used of sample correlation coefficient. The generalized T2- statistics. Classification of observations. Procedures of classification into one of two or three specified multicariate normal populations. Discriminant function when populations are unknown. Principal components and factor analysis

STA 464.1 Regression Analysis and Model Building

Multiple linear regression models, polynomial regresson. Tests of independence and goodness-of- fit. Use of Dummy variables. Non-linearity in parameters requiring simpletransformation. Partial and conditional regression and correlation models. Canonical correlation. Tests of independence of regression coefficients. Other problems associated with “Best Regression Models” Bayesian estimates, Checking the model, goodness of fit test. Fitting a straight line, linear models, parameter estimates tests of significance and confidence intervals, residual plot and tests of fit.

Multiple linear regression models, polynomial regresson. Tests of independence and goodness-of- fit. Use of Dummy variables. Non-linearity in parameters requiring simpletransformation. Partial and conditional regression and correlation models. Canonical correlation. Tests of independence of regression coefficients. Other problems associated with “Best Regression Models” Bayesian estimates, Checking the model, goodness of fit test. Fitting a straight line, linear models, parameter estimates tests of significance and confidence intervals, residual plot and tests of fit.

STA 468.1 Bayesian Inference

Bayes’ Theory. Posterior distributions. One parameter cases in some standard continuous discrete distributions. Point and interval estimation. Prediction of future observation. Choice of priors: natural conjugate families of prior distribution, simple non-informative priors. Comparison of the means and variance of two normal and Poisson distributions, linear regression. Tests of hypothesis.

Bayes’ Theory. Posterior distributions. One parameter cases in some standard continuous discrete distributions. Point and interval estimation. Prediction of future observation. Choice of priors: natural conjugate families of prior distribution, simple non-informative priors. Comparison of the means and variance of two normal and Poisson distributions, linear regression. Tests of hypothesis.

CSC 486.1 Systems Analysis And Design

Introduction to systems analysis, structured and object-oriented analysis and design, structured and object-oriented tools, the systems life cycle. Organizational structure. Systems investigation. Feasibility studies. Determination and evaluation of alternatives designs of input, output and file structures. Documentation. Choice of system characteristics (Hardware and software). Testing, conversion. Parallel runs. Evaluation of system performance. Maintenance.

Introduction to systems analysis, structured and object-oriented analysis and design, structured and object-oriented tools, the systems life cycle. Organizational structure. Systems investigation. Feasibility studies. Determination and evaluation of alternatives designs of input, output and file structures. Documentation. Choice of system characteristics (Hardware and software). Testing, conversion. Parallel runs. Evaluation of system performance. Maintenance.

CSC 480.1 Database Management

Basic concepts. Data integration. Data independence. Functions and architecture of a DBMS. Data models. Storage structures and access stractegies. Relations and relational operations. Relational algebra and calculus. Normalization. Security and integrity issues. Relational systems, INGRES, DBASE entity – relationship model. E-R. diagrams. Semantic and semantic nets. IKBS’s

Basic concepts. Data integration. Data independence. Functions and architecture of a DBMS. Data models. Storage structures and access stractegies. Relations and relational operations. Relational algebra and calculus. Normalization. Security and integrity issues. Relational systems, INGRES, DBASE entity – relationship model. E-R. diagrams. Semantic and semantic nets. IKBS’s

STA 465.1 Sampling Techniques

Ratio, Regression and Difference estimation procedures. Double sampling. Interpreting scheme. Multiphase and multistage sampling, cluster sampling with unequal sizes: problem of optimal allocation with more than one item. Further stratified sampling.

Ratio, Regression and Difference estimation procedures. Double sampling. Interpreting scheme. Multiphase and multistage sampling, cluster sampling with unequal sizes: problem of optimal allocation with more than one item. Further stratified sampling.

CSC 498.1 Computer Network and Data Communication

Introduction, waves Fourier analysis, measure of communication channel characteristics, transmission media, noise and distortion, modulation and demodulation; multiplexing TDM FDM and FCM. Parallel and serial transmission (synchronous vs anachronous). Bus structures and loop systems, computer network. Examples and design consideration: data switching principles; broadcast techniques; network structure for packet switching, protocols, description of network e.g. ARPANET, DSC etc.

Introduction, waves Fourier analysis, measure of communication channel characteristics, transmission media, noise and distortion, modulation and demodulation; multiplexing TDM FDM and FCM. Parallel and serial transmission (synchronous vs anachronous). Bus structures and loop systems, computer network. Examples and design consideration: data switching principles; broadcast techniques; network structure for packet switching, protocols, description of network e.g. ARPANET, DSC etc.

CSC 482.1 Compiler Construction

Translators; compilers, assemblers, interpreters, preprocessors. Functional blocks of a complier. The compilation process – Lexical analysis, syntax and semantic analysis. Code generation, code optimization. Error detection and recovery. Lexical analysis, transition diagrams. Review of context – free grammars. Parsing context –free expressions. Top-down and bottom-up praising. LL(K) & LR parsing. Operator –precedence paring. Symbol table structures.

Translators; compilers, assemblers, interpreters, preprocessors. Functional blocks of a complier. The compilation process – Lexical analysis, syntax and semantic analysis. Code generation, code optimization. Error detection and recovery. Lexical analysis, transition diagrams. Review of context – free grammars. Parsing context –free expressions. Top-down and bottom-up praising. LL(K) & LR parsing. Operator –precedence paring. Symbol table structures.

STA 461.1 Non-Parametric Methods

Non parametric: Order statistics and their distributions. Kolmogorov type of tests statistic. Common non-parametric test including runs, sing rank order and rank correlation. Null distribution: Bivariate normal distribution, the gamma, chi-square, 2 types of beta distribution of functions of random variables. Probability integral transformation. Bivariate moment generating functions, univariate characteristic functions. Various modes of convergence, laws of large numbers and the central limit theorem using characteristic functions.

Non parametric: Order statistics and their distributions. Kolmogorov type of tests statistic. Common non-parametric test including runs, sing rank order and rank correlation. Null distribution: Bivariate normal distribution, the gamma, chi-square, 2 types of beta distribution of functions of random variables. Probability integral transformation. Bivariate moment generating functions, univariate characteristic functions. Various modes of convergence, laws of large numbers and the central limit theorem using characteristic functions.

STA 469.1 Decision Theory

Empirical sources of knowledge-hypothesis, observation and experiment. Deductive sources of knowledge and scientific attitude. The concept of causation. Probability, a brief historical treatment to show conflicting definitions. Bayesian statistics and the decision making. Utility functions and their properties. Role of uncertainty. Bayes Strategies. Problems of prior and posterior distributions: value of prior information Minimax strategies. Statistical inference Theory of games.

Empirical sources of knowledge-hypothesis, observation and experiment. Deductive sources of knowledge and scientific attitude. The concept of causation. Probability, a brief historical treatment to show conflicting definitions. Bayesian statistics and the decision making. Utility functions and their properties. Role of uncertainty. Bayes Strategies. Problems of prior and posterior distributions: value of prior information Minimax strategies. Statistical inference Theory of games.

CSC 483.1 Algorithms and Complexity Analysis

Design and specification of algorithms. Efficiency of algorithms: running and memory usage, polynomial time and super-polynomial time algorithms. Analysis of algorithms: best-case, average-case, worst-case analyses. Asymptotic programming, randomized algorithms. Searching: sequential and binary search. Sorting algorithms: bubble, insertion quick sort, merge sort, heap sort. Exponential algorithms: performance optimization.

Design and specification of algorithms. Efficiency of algorithms: running and memory usage, polynomial time and super-polynomial time algorithms. Analysis of algorithms: best-case, average-case, worst-case analyses. Asymptotic programming, randomized algorithms. Searching: sequential and binary search. Sorting algorithms: bubble, insertion quick sort, merge sort, heap sort. Exponential algorithms: performance optimization.

MTH 430.1 Algebraic Topology

Brief review of basics from general topology L-connectedness, components, paths, path-connectedness, path-components, the set (x). Algebraic background, including free groups, groups defined by deneraters and relations, exact sequences. Homotopy, homotopy equivalence, retracts and deformation retracts, contractible spaces, the fundamental group. Simplexes, simplicial simplexes, subcomplexes, simplical maps derived (barycentric) subdivision, simplical approximation theorem. The edge-path group, its isomonphism with the fundamental group, calculations of 1 (k) especially for closed surfaces, Brouwer fixed point theorem in the plane. Simplicial homology groups. The induced homoorphism f* when f is simplicial, outline proof of topological invariance of the homology groups. Calculation of Hn(Sm), proof that Sn and Sm are not homotopy equivalent and Rn and Rm are not homonorphic (n=m), generalized Brouwer fixed point theorem. Mayer-Vietoris sequence calculation of homology groups, especially for closed surfaces.

Brief review of basics from general topology L-connectedness, components, paths, path-connectedness, path-components, the set (x). Algebraic background, including free groups, groups defined by deneraters and relations, exact sequences. Homotopy, homotopy equivalence, retracts and deformation retracts, contractible spaces, the fundamental group. Simplexes, simplicial simplexes, subcomplexes, simplical maps derived (barycentric) subdivision, simplical approximation theorem. The edge-path group, its isomonphism with the fundamental group, calculations of 1 (k) especially for closed surfaces, Brouwer fixed point theorem in the plane. Simplicial homology groups. The induced homoorphism f* when f is simplicial, outline proof of topological invariance of the homology groups. Calculation of Hn(Sm), proof that Sn and Sm are not homotopy equivalent and Rn and Rm are not homonorphic (n=m), generalized Brouwer fixed point theorem. Mayer-Vietoris sequence calculation of homology groups, especially for closed surfaces.

MTH 455.1 General Relativity

General theory_ principles of equivalence, Riemann_Christorffel ecurvature tensor, field equation of the general theory and their rigorous solutions, experimental tests, and equations of motion; and unified field theories. Weyl’s gauge-invariant geometry, Kaluza’s five dimensional theory and projective field theories, and a generalization of Kaluza’s theory.

General theory_ principles of equivalence, Riemann_Christorffel ecurvature tensor, field equation of the general theory and their rigorous solutions, experimental tests, and equations of motion; and unified field theories. Weyl’s gauge-invariant geometry, Kaluza’s five dimensional theory and projective field theories, and a generalization of Kaluza’s theory.

MTH 432.1 Functional Equations

Equation for functions of a single variables, methods of Solutions, Continuity, Monotonuity and uniqueness of solution of the form F(G(x,y))=F(f(x),y) and similar types. Cauchy’s and Jensen’s functional equation and applications. D’Alemburt’s functional equations and application. Functional Equations and addition theorems. Plexider’s functional Equations and related ones. Wilson’s generalizations of D’Alemburt’s equation.

Equation for functions of a single variables, methods of Solutions, Continuity, Monotonuity and uniqueness of solution of the form F(G(x,y))=F(f(x),y) and similar types. Cauchy’s and Jensen’s functional equation and applications. D’Alemburt’s functional equations and application. Functional Equations and addition theorems. Plexider’s functional Equations and related ones. Wilson’s generalizations of D’Alemburt’s equation.

MTH 492.2 Numerical Methods

Solution of ordinary Differential Equations: Linear equations, finite difference method for boundary value problems. Non-linear equations, Runge-Kutta and Shooting algorithms. Method of quasi-linearization. Partial differential equation: Parabolic equations, explicit finite, differences scheme. Implicit scheme. Elliptic and hyperbolic equations and finite differences. Finite element methods.

Solution of ordinary Differential Equations: Linear equations, finite difference method for boundary value problems. Non-linear equations, Runge-Kutta and Shooting algorithms. Method of quasi-linearization. Partial differential equation: Parabolic equations, explicit finite, differences scheme. Implicit scheme. Elliptic and hyperbolic equations and finite differences. Finite element methods.

MTH 412.2 Fields and Galois Theory

Fields, homomorphisms of fields. Finite fields. Prime fields. Guotient rings which are fields. Irreducibility Esenstein criterion. Field extensions degree of an extension, minimum polymonial algebraic and transcendental extensions, straightedge and compass construction. Algebraic closure of a field. The Jacobsor Bourbaki correspondence.

Fields, homomorphisms of fields. Finite fields. Prime fields. Guotient rings which are fields. Irreducibility Esenstein criterion. Field extensions degree of an extension, minimum polymonial algebraic and transcendental extensions, straightedge and compass construction. Algebraic closure of a field. The Jacobsor Bourbaki correspondence.

MTH 424.2 Ordinary Differential Equations II

Existence and uniqueness theorem and dependence of solution on initial data and parameter,

properties and solution storm and Picone Comparison theorem. Linear System: Floquets theory. Non-linear Systems: Stability theory. Integral equations. Methods of Successive approximations Neiman’s series. Resolvent Kernel, Votterra equation Application to ODE.

MTH 422.2 Measures and Integration

Countability of sets and cardinal numbers, out measure measurable set and Lebseque measure, measureable functions, the Lebesque integral, convergence of sequence of measure le functions General Lebesque integral. Lp spaces, riesz-Fischer theorem.

Countability of sets and cardinal numbers, out measure measurable set and Lebseque measure, measureable functions, the Lebesque integral, convergence of sequence of measure le functions General Lebesque integral. Lp spaces, riesz-Fischer theorem.

MTH 470.2: Research Project

Students are expected to carry out research works in areas that are of interest to the students and are related to the mathematical knowledge and skills gained during the course work.The research work shall be in line with the degree to be awarded. The research work shall be summarised in a project report to be examined by internal and external examiners.

Students are expected to carry out research works in areas that are of interest to the students and are related to the mathematical knowledge and skills gained during the course work.The research work shall be in line with the degree to be awarded. The research work shall be summarised in a project report to be examined by internal and external examiners.

MTH 450.2 Continuum Mechanics

Tensor Calculus of double fields. Deformation and its derivative tensor. Kinematics of lines, surfaces and volumes, Analysis for Stress. Isotropy groups of material. Equations of balance with and without discontinuity surfaces. Thermoechanical constitutive relations for various materials with the without kinematics constaints. Solution of simple equations of motion of selected materials.

Tensor Calculus of double fields. Deformation and its derivative tensor. Kinematics of lines, surfaces and volumes, Analysis for Stress. Isotropy groups of material. Equations of balance with and without discontinuity surfaces. Thermoechanical constitutive relations for various materials with the without kinematics constaints. Solution of simple equations of motion of selected materials.

MTH 414.2 Introduction to Semigroup Theory

Basic Notions of Semigroups. Monogenic semigroups. Ordered Sets, seim-lattices and lattices. Congruences. Three semigroups. Grenn’s relations. The structure of D_classes. Regular D_classes. Regular Primitive idempotents. Semilattice of groups. Invserse semigroups

Basic Notions of Semigroups. Monogenic semigroups. Ordered Sets, seim-lattices and lattices. Congruences. Three semigroups. Grenn’s relations. The structure of D_classes. Regular D_classes. Regular Primitive idempotents. Semilattice of groups. Invserse semigroups

MTH 458.2 Control Theory

Dynamical systems in the state space, Reachability, stabilizability and detecability. Equivalences of controllability and pole assignability. The Calculus of variations. Generalized Huygen’s principle. Reachable sets. Optimal Control with quadratics cost. Pontryagin’s maximum principles. The Algebraic Riccati equation. Lyapunov stability. Applications to Economic stabilization, planning, manpower development, resource allocation under constraints etc.

Dynamical systems in the state space, Reachability, stabilizability and detecability. Equivalences of controllability and pole assignability. The Calculus of variations. Generalized Huygen’s principle. Reachable sets. Optimal Control with quadratics cost. Pontryagin’s maximum principles. The Algebraic Riccati equation. Lyapunov stability. Applications to Economic stabilization, planning, manpower development, resource allocation under constraints etc.

MTH 418.2 Rings and Modules

Modules –Basic Notions, Submodules, homomorphism of modules. Artunian and Noetherian modules. Jordan-Holder theorem. The krull Schmidt theorem. Rings_Primitive and Semiprimitive rings, radical of a ring. Density theorems and Artinian rings. The structure of algebras. Prime ideals, Ni-radical. Prime spectrum of a commutative rings. The basis theorem. Deurapostition of rings and modules

Modules –Basic Notions, Submodules, homomorphism of modules. Artunian and Noetherian modules. Jordan-Holder theorem. The krull Schmidt theorem. Rings_Primitive and Semiprimitive rings, radical of a ring. Density theorems and Artinian rings. The structure of algebras. Prime ideals, Ni-radical. Prime spectrum of a commutative rings. The basis theorem. Deurapostition of rings and modules

STA 474.2 Probability Theory

Probability spaces, measures and distribution. Distribution of random variables as measureable functions. Product spaces; product of measurable spaces, product probabilities. Independence and expectation of random variables; weak convergence, convergence almost everywhere, convergence in nth mean, central limit theorem, laws of large number. Characteristic function and Laplace transforms.

¬¬¬¬¬¬MTH 454.2 Electromagnetic Theory

Review of curvilinear coordinates.

Electrostatics-Gauss’s law, electrostatic scalar potential, dipoles and quadrupoles. Solution of Laplace equation in Cartestian, cylindrical and spherical polar coordinates. Two-dimensional problems and complex variable methods. Magnetic field of currents- Eiot Savat Law. Complete Maxwell’s equations. Vector potential Special Relativity and Maxwell’s equations.

Electromagnetic Waves.

Probability spaces, measures and distribution. Distribution of random variables as measureable functions. Product spaces; product of measurable spaces, product probabilities. Independence and expectation of random variables; weak convergence, convergence almost everywhere, convergence in nth mean, central limit theorem, laws of large number. Characteristic function and Laplace transforms.

¬¬¬¬¬¬MTH 454.2 Electromagnetic Theory

Review of curvilinear coordinates.

Electrostatics-Gauss’s law, electrostatic scalar potential, dipoles and quadrupoles. Solution of Laplace equation in Cartestian, cylindrical and spherical polar coordinates. Two-dimensional problems and complex variable methods. Magnetic field of currents- Eiot Savat Law. Complete Maxwell’s equations. Vector potential Special Relativity and Maxwell’s equations.

Electromagnetic Waves.

MTH 416.2 Lattices and Algebraic System

Lattices-Basic notions of lattices distributive lattices, modular and non lattices. Sublattices and homomorphisms of lattices. Category Theory: Basic Notion of categories, objects and maps. Functors and natural transformations Concrete Examples of categories, Universal subalgebras, homomrphism of algebras products. Congruences, congruence lattice on algebras. Free algebras, concrete examples universal algebras. Subdirect products

Lattices-Basic notions of lattices distributive lattices, modular and non lattices. Sublattices and homomorphisms of lattices. Category Theory: Basic Notion of categories, objects and maps. Functors and natural transformations Concrete Examples of categories, Universal subalgebras, homomrphism of algebras products. Congruences, congruence lattice on algebras. Free algebras, concrete examples universal algebras. Subdirect products

STA 478.2 Stochastic Processes

Introduction to Stochastic and definition of terms, e.g. absorbing and reflecting barriers. Random walk. Examples of random walk with reflecting and absorbing barriers, and examples from queuing theory. The general Markov Chain, a two-state Markov Chain, the classification of states and the limit theorem, closed set of states Stationary transition probabilities. Morkov processes with discrete state in continuous time, the Poission process. Pre-requisite MTH 360.1, MTH 320.1.

Introduction to Stochastic and definition of terms, e.g. absorbing and reflecting barriers. Random walk. Examples of random walk with reflecting and absorbing barriers, and examples from queuing theory. The general Markov Chain, a two-state Markov Chain, the classification of states and the limit theorem, closed set of states Stationary transition probabilities. Morkov processes with discrete state in continuous time, the Poission process. Pre-requisite MTH 360.1, MTH 320.1.

STA 476.2 Econometric Methods

Nature and quality of econometrics data and use of econometric models. Problems of regression analysis; multicollinearity, heteroscedasticity, Autocorrelation, Errors in Variables and their effects. Time as a variable, Dummy Variable, Grouped data. Lagged variables and distributed lag models; application to cross-section and time series data, demand studies, measurement of production, consumption and investment functions. Simultaneous equation and identification, Bias in reduced form. Estimation: Indirect least squares and two –stage lease squares. Ideas of model specification and specification error. Maximum likelihood methods applied to econometric.

Nature and quality of econometrics data and use of econometric models. Problems of regression analysis; multicollinearity, heteroscedasticity, Autocorrelation, Errors in Variables and their effects. Time as a variable, Dummy Variable, Grouped data. Lagged variables and distributed lag models; application to cross-section and time series data, demand studies, measurement of production, consumption and investment functions. Simultaneous equation and identification, Bias in reduced form. Estimation: Indirect least squares and two –stage lease squares. Ideas of model specification and specification error. Maximum likelihood methods applied to econometric.

STA 475.2 Analysis of Categorical Data

Analysis of simple, double and multiple classification of balanced data in crossed and nested arrangement. Analysis of two-ways, three-ways contingency tables for test of homogeneity, independence and interactions. Analysis involving incomplete tables, missing values, etc. analysis of variance involving unbalanced data. Multi-variate analysis of variance. Analysis of multi-factor, multi-response of variance such as missing observations. Non-normality, heterogeneity of variance,

Analysis of simple, double and multiple classification of balanced data in crossed and nested arrangement. Analysis of two-ways, three-ways contingency tables for test of homogeneity, independence and interactions. Analysis involving incomplete tables, missing values, etc. analysis of variance involving unbalanced data. Multi-variate analysis of variance. Analysis of multi-factor, multi-response of variance such as missing observations. Non-normality, heterogeneity of variance,

STA 473.2 Biometry II

Purpose, history and structure of biological assays. Types of Bioassays. Feller’s theorem and its analogurs. The Behrens distribution. Dillution assays adjustments for body weight. Direct assay with covariance. Design and criticisms of direct assays. Indirect asays. The dose-response regression.

Purpose, history and structure of biological assays. Types of Bioassays. Feller’s theorem and its analogurs. The Behrens distribution. Dillution assays adjustments for body weight. Direct assay with covariance. Design and criticisms of direct assays. Indirect asays. The dose-response regression.

STA 477.2 Simulation and Modeling

Basic Concepts: Philosophy, development implementation and design of simulation models.

Pseudo-Random Numbers: Generation of random numbers, Uniform distribution and its importance to simulation.

Simulation Techniques: Mid-square, mid-product, Fibonacci, Congruential, mixed method, multiplicative etc.

Tests for Random Number Generator: Frequency, Gap, Runs, Poker etc.

Simulation Languages: Overview and Comparison, GPSS, GASP, SIM ULA, DYNAMO etc. Simulation Modeling: Queues, sales of insurance policies production line maintenance.

Basic Concepts: Philosophy, development implementation and design of simulation models.

Pseudo-Random Numbers: Generation of random numbers, Uniform distribution and its importance to simulation.

Simulation Techniques: Mid-square, mid-product, Fibonacci, Congruential, mixed method, multiplicative etc.

Tests for Random Number Generator: Frequency, Gap, Runs, Poker etc.

Simulation Languages: Overview and Comparison, GPSS, GASP, SIM ULA, DYNAMO etc. Simulation Modeling: Queues, sales of insurance policies production line maintenance.

STA 472.2 Time Series Analysis

Components of time series, measurement of trend, the seasonal index, the cyclical component and random fluctuations. Serial correlation, correlogram. Stationary time series, estimation of mean and their covariance function. Linear prediction in time series, autoregressive process. Moving average process. Seasonal models. Models identification

Components of time series, measurement of trend, the seasonal index, the cyclical component and random fluctuations. Serial correlation, correlogram. Stationary time series, estimation of mean and their covariance function. Linear prediction in time series, autoregressive process. Moving average process. Seasonal models. Models identification

CSC 492.2 Computer Graphics

Hardware aspect; plotters microfilm, plotters displays, graphic-tablets, light pens, other graphical input aids. Facsimile and its problems. Refresh display, refresh buggers, changing images light pen interaction. Two and three dimensional transformation perspective. Clipping algorithms, hidden live removal, Holden surface removal; warrock’s method, shading, data reduction for graphical input. Institution to hand writing and character recognition. Curve synthesis and fitting. Contouring ring structures versus doubly linked lists. Hierarchical structures; Data structure; organization for inter-active graphics.

CSC 494.2 Introductions to Artificial Intelligence

Definition of Artificial Intelligence. Scope and applications of Artificial Intelligence. Problem solving techniques; searching. Logic and inference knowledge-base systems. Natural Languages. Pattern Recognition and vision systems. Expect system-architecture, construction and use.

Definition of Artificial Intelligence. Scope and applications of Artificial Intelligence. Problem solving techniques; searching. Logic and inference knowledge-base systems. Natural Languages. Pattern Recognition and vision systems. Expect system-architecture, construction and use.

CSC 493.2 Internet and Web applications

The definition of the internet. The origin, history and development of the internet. The network protocol used on the Internet-the internet protocol. The Five layers of the TCP/IP protocol, stack-application layer, transport layer, network layer, data link layer, physical layer. The internet components: Most used facilities in the internet; Email, U-tube, View data system, Telecom fencing. etc The Internet Service provider (ISP), Intranets, Extranets, Web master. Governance of the messaging (e-mail), electronic data interchange (EDI), Area of internet application-teleworking, distance education, virtual (e-learning) classroom, entertainment, sports, news, e-governance, etc Internet age system. Advantage and Disadvantages of the Internet. The lecturer may opt to use HTML or JAVA scripts for illustration.

The definition of the internet. The origin, history and development of the internet. The network protocol used on the Internet-the internet protocol. The Five layers of the TCP/IP protocol, stack-application layer, transport layer, network layer, data link layer, physical layer. The internet components: Most used facilities in the internet; Email, U-tube, View data system, Telecom fencing. etc The Internet Service provider (ISP), Intranets, Extranets, Web master. Governance of the messaging (e-mail), electronic data interchange (EDI), Area of internet application-teleworking, distance education, virtual (e-learning) classroom, entertainment, sports, news, e-governance, etc Internet age system. Advantage and Disadvantages of the Internet. The lecturer may opt to use HTML or JAVA scripts for illustration.