Course Modules

The Stress areas are as follows

  • Service Courses
  • Pure Mathematics (Algebra, Geometry)
  • Pure Mathematics (Calculus, Analysis, Differential Equations)
  • Applied Mathematics (Theoretical and Applied Mechanics, and mathematical Physics)
  • Mathematical Methods

Standard Four-Year Programme

First Year Mathematics
First Semester
Major Courses
MTH 111 Elementary Mathematics I 3
MTH 121 Elementary Mathematics II 3
Required Ancillary Course
STA 205 Statistics for Physical Sciences 2
COS 101 Introduction to Computer Science 2
General Study Courses
GSP 101 Communication in English I 2
GSP 111 The Use of Library and Study Skills 2
Elective Courses
Any 4-5 unit from the following: 4/5
PHY 125 Fundamentals of Physics I 3
PHY 193 Practical Physics II 2
CHM 101 Basic Principles of Chemistry I 2
CHM 171 Basic Practical Chemistry 2
STA 111 Probability I 2
STA 131 Inference I 2
BIO 151 General Biology I 3
18/19
Second Semester
Major Courses
MTH 122 Elementary Mathematics III 3
MTH 132 Elementary Mechanics I 3
Required Ancillary Courses
STA 206 Statistics for Physical Sciences 2
General Study Courses
GSP 102 Communication in English II 2
Elective Courses
Any 4-5 units from the following: 6/7
PHY 136 Fundamental of Physics 3
PHY 156 Fundamental of Physics III 2
CHM 112 Basic Principle of Physical Chemistry 2
CHM 122 Basic Principle of Organic Chemistry 2
GLG 142 Earth History 3
STA 112 Probability II 2
STA 132 Inference II 2
STA 134 Laboratory for Inference I 2
16/17
Second Year Mathematics
First Semester
Major Courses
MTH 211 Set, Logic and Algebra 3
MTH 215 Linear Algebra I 2
MTH 221 Real Analysis I 3
MTH 231 Elementary Mechanics II 2
Required Ancillary Courses
STA 211 Probability III 2
COS 201 Computer Programming I 2
General Study Courses
GSP 201 Basic Concepts &Theory of Peace 2
GSP 207 Logic, Philosophy and Human Existence 2
Second Semester
Major Courses
MTH 218 Three- Dimensional Analytic Geometry 2
MTH 216 Linear Algebra II 2
MTH 222 Elementary Differential Equations I 3
MTH 224 Introduction to Numerical Analysis 3
MTH 242 Mathematical Methods I 3
MTH 242 Mathematical Methods I 3
STA 212 Probability IV 2
General Study Courses
GSP 202 Issues in Peace and Conflict Resolution 2
GSP 208 Nigerian People and Culture 2
Third Year Mathematics
First Semester
Major Courses
MTH 311 Abstract Algebra I 3
MTH 321 Metric Space Topology 3
MTH 327 Elementary Differential Equation II 3
MTH 323 Complex Analysis I 3
MTH 331 Introduction to Mathematical Modelling 3
Elective Courses
Any 2-3 units from the following 2/3
*MTH 313 Geometry I 2
MTH 329 Calculus in RN 3
MTH 337 Optimization Theory I 2
MTH 339 Analytic Dynamics 2
MTH 335 Introduction to Operation Research 3
**MTH 341 Discrete Mathematics I 2
STA 311 Probability V 2
STA 321 Distribution Theory 2
STA 331 Statistical Inference IV 2
COS 333 Systems Analysis and Design 2
17/18
*To be taken with MTH 314
**To be taken with MTH 342
SECOd Semester
Major Courses
MTH 312 Abstract Algebra II 3
MTH 324 Vector and Tensor Analysis 3
MTH 328 Complex Analysis II 3
MTH 326 Real Analysis II 3
Elective Courses
Any 4-5 units from the following    4/5
MTH 314 Geometry II 2
MTH 316 Differential Geometry 3
MTH 338 Optimization Theory II 2
MTH 336 Dynamics of Rigid Body 3
MTH 338 Special Theory of Relativity 4
MTH 342 Discrete Mathematics II 2
MTH 344 Numerical Analysis I 3
STA 312 Probability VI 2
STA 332 Inference VI 2
COS 332 Operating System II 2
16/17
Fourth Year Mathematics
First Semester
Major Courses
MTH 421 Ordinary Differential Equation 3
MTH 429 Functional Analysis 3
MTH 425 Lebesgue Measure and Integration 3
Elective Courses
Any 6-7 units from the following 6/7
MTH 427 Field Theory in Mathematical Physics 3
MTH 439 Analytic Dynamics II 3
MTH 437 System Theory 4
MTH 443 Numerical Analysis II 3
MTH 441 Mathematical Methods II 3
15/16
Second Semester
Major Courses
MTH 428 Partial Differential Equations 3
MTH 424 General Topology 3
MTH 452 Project 4
Elective Courses
Any 6-7 units from the Following: 6/7
MTH 412 Abstract III 3
MTH 432 General Theory of Relativity 4
MTH 438 Electromagnetism 3
MTH 436 Fluid Dynamics 3
MTH 434 Elasticity 3
MTH 444 Numerical Analysis III 3
16/17

Three Year Standard Programme

The three year-standard programme is the same as the four-year standard programme excluding the first year. However, the direct entry students are required to take GSP 101, GSP 102, GSP 207 and GSP 208 during their first year.

Service Courses Intended for Specified Departments/Faculties

First Semester
MTH 201 Advanced Mathematics I 3
(Primarily intended for students of Accountancy and Management)
MTH 203 Advanced Mathematics III 3
Primarily intended for students of Surveying Students)
MTH 205 Advanced Mathematics V 2
MTH 207 Advanced Mathematics VII 2
(Primarily intended for Engineering Students)
Second Semester
(Primarily intended for Accountancy and Management Students)
MTH 202 Advanced Mathematics II 3
Primarily intended for students of Surveying Students)
MTH 204 Advanced Mathematics IV 2
MTH 206 Advanced Mathematics VI 2
MTH 208 Advanced Mathematics VIII 2
Primarily intended for students of Surveying Students)
First Year MATHEMATICS/CHEMISTRY
First Semester
Major Courses
MTH 111 Elementary Mathematics I 3
MTH 121 Elementary Mathematics II 3
CHM 101 Basic Principles of Inorganic Chemistry 2
CHM 171 Basic Practical Chemistry 2
Required Ancillary Courses
PHY 115 General Physics for Physical Sciences I 2
PHY 116 General Physics for Physical Sciences II 2
General Study Courses
GSP 101 Communication in English I 2
GSP 111 The Use of Library and Study Skills 2
Total Units 18
Second Semester
Major Courses
MTH 122 Elementary Mathematics III 3
CHM 112 Basic Principle of Physical Chemistry 2
CHM 122 Basic Principle of Organic Chemistry 2
Required Ancillary Courses
PHY 118 General Physics for Physical Sciences III 2
MTH 131 Elementary Mechanics I 3
General Study Courses
GSP 102 Use of English II 2
Total Units 14
Second Year MATHEMATICS/CHEMISTRY
First Semester
Major Courses
MTH 211 Set, Logic and Algebra 3
MTH 215 Linear Algebra I 2
MTH 221 Real Analysis I 3
CHM 201 General Inorganic Chemistry 2
CHM 211 General Physical Chemistry 2
CHM 221 General Inorganic Chemistry I 2
CHM 273 Practical Organic Chemistry I 2
Required Ancillary Courses
CS 101 Introduction to Computer Science 2
General Study Courses
GSP 201 Basic Concepts &Theory of Peace 2
GSP 207 Logic, Philosophy and Human Existence 2
Total Units    22
Second Semester
Major Courses
MTH 216 Linear Algebra II 2
MTH 222 Elementary Differential Equations I 3
MTH 242 Mathematical Methods I 3
CHM 222 General Inorganic Chemistry II 2
CHM 232 Analytic Chemistry 2
CHM 272 Practical Physical Chemistry I 2
CHM 274 Practical Inorganic Chemistry I 2
Required Ancillary Courses
GSP 202 Issues in Peace and Conflict Resolution 2
GSP 208 Nigerian People and Culture 2
Total Units 20
Third Year MATHEMATICS/CHEMISTRY
First Semester
Major Courses
MTH 311 Abstract Algebra I 3
MTH 323 Complex Analysis I 3
CHM 301 Inorganic Chemistry I 2
CHM 311 Physical and Structural Chemistry I 2
Required Ancillary Courses
COS 201 Computer Programming I 2
Elective Courses
Any 4-5 units from the following
GEOL 103 Basic and Applied Geology for Environmental and Physical   Sciences 3
GEOL 213 Optical Mineralogy 2
STA 205 Statistics for Physical Sciences and Engineering I 2
Total Units 16/17
Second Semester
Major Courses
MTH 312 Abstract Algebra II 3
MTH 326 Real Analysis II 3
CHM 302 Inorganic Chemistry II 2
CHM 312 Physical and Structural Chemistry II 2
CHM 314 Physical and Structural Chemistry III 2
Required Ancillary Courses
PHY 262 Introduction to Atomic and Nuclear Physics 3
Elective Courses
Any 5 units from the following       5
COS 202 Computer Programming II 3
GEOL 212 Crystallography and Mineralogy 2
GEOL 141 Earth History 3
Total Units 20
Fourth Year MATHEMATICS/CHEMISTRY
First Semester
Major Courses
MTH 321 Metric Space Topology 3
MTH 327 Elementary Differential Equation II 3
MTH        337 Optimization Theory I      2
CHM 321 Organic Chemistry I 2
CHM 374 Applied Spectroscopy 2
CHM 411 Advanced Physical Chemistry I 2
CHM 431 Modern Analytical Techniques 2
MTH/ CHM 452/492 Project 4/6
Total Units 20/22
Second Semester  
Major Courses  
MTH 324 Vector and Tensor Analysis        3
MTH 328 Complex Analysis II 3
CHM 322 Organic Chemistry II 2
CHM 323 Organic Chemistry III 2
CHM 412 Advanced Physical Chemistry II 2
CHM 372 Practical Physical Chemistry II 2
CHM 402 Advanced Inorganic Chemistry II 2
Total Units 16

 

 

First Year MATHEMATICS/ECONOMICS
First Semester
Major Courses
MTH 111 Elementary Mathematics I 3
MTH 121 Elementary Mathematics II 3
ECO 101 Principles of Economics I 2
ECO 131 Introduction to Economics Statistics I 2
Required Ancillary Course
STA 111 Probability I 2
STA 131 Inference I 2
COS 101 Introduction to Computer Science 2
General Studies Courses
GSP 101 Communication in English I 2
GSP 111 The Use of Library and Study Skills 2
Total Units 20
Second Semester
Major Courses
MTH 122 Elementary Mathematics III 3
ECO 102 Principles of Economics II 2
ECO 132 Introduction to Economics Statistics II 2
Required Ancillary Course
STA 112 Probability II 2
STA 132 Inference II 2
STA 172 Statistical Computing I 2
General Studies Courses
GSP 102 Communication in English II 2
Total Units 15
Second Year MATHEMATICS/ECONOMICS
First Semester
Major Courses
MTH 211 Set, Logic and Algebra 3
MTH 215 Linear Algebra I 2
MTH 221 Real Analysis I 3
ECO 201 Intermediate Microeconomic Theory I 2
ECO 203 Macroeconomic Theory I 2
ECO 281 Structure of Nigerian Economy I 2
General Study Courses
GSP 201 Basic Concepts &Theory of Peace 2
GSP 207 Logic, Philosophy and Human Existence 2
Total Units      18
Second Semester
Major Courses
MTH 216 Linear Algebra II 2
MTH 222 Elementary Differential Equations I 3
MTH 224 Introduction to Numerical Analysis 3
ECO 202 Intermediate Microeconomic Theory II 2
ECO 204 Macroeconomic Theory II 2
ECO 281 Structure of Nigerian Economy II 2
General Study Courses
GSP 202 Issues in Peace and Conflict Resolution 2
GSP 208 Nigerian People and Culture 2
Total Units 18
Third Year MATHEMATICS/ECONOMICS
First Semester
Major Courses
MTH 321 Metric Space Topology 3
MTH 323 Complex Analysis I 3
MTH 337 Optimization Theory I 2
*ECO 301 Intermediate Microeconomic Theory I 2
*ECO 361 Development Economics 2
ECO 391 Research Methods in Economics I 2
Required Ancillary Courses
STA 361 Probability III 2
STA 231 Inference II 2
Total Units 20
Second Semester
Major Courses
MTH 326 Real Analysis II 3
MTH 328 Complex Analysis II 3
MTH 338 Optimization Theory II 2
ECO 332 Introduction to Econometrics 2
ECO 302 Intermediate Microeconomic Theory II 4
Elective Courses
Any 2 units from the following    2
ECO 334 Mathematical Economics I 2
ECO 324 Financial Institution 2
Total Units 16
Fourth Year MATHEMATICS/ECONOMICS
First Semester
Major Courses
MTH 331 Introduction to Mathematical Modelling 3
MTH 337 Elementary Differential Equations II 3
MTH 429 Functional Analysis 3
ECO 401 Advanced Microeconomic Theory and Policy I 2
ECO 403 Advanced Macroeconomic Theory and Policy I 2
ECO 461 Problems and Policies of Development 2
ECO 465 Economic Planning I 2
ECO 475 Project Evaluation I 2
Total Units 16
Second Semester  
Major Courses  
MTH 324 Vector and Tensor Analysis 3
ECO 402 Advanced Microeconomic Theory and Policy II 2
ECO 404 Advanced Macroeconomic Theory and Policy II 2
ECO 466 Economic Planning II 2
ECO 476 Project Evaluation II 2
MTH/ECO 452/476 Project    4/6
Total Units 15/17

 

First Year MATHEMATICS/PHYSICS
First Semester
Major Courses
MTH 111 Elementary Mathematics I 3
MTH 121 Elementary Mathematics II 3
PHY 121 Fundamentals of Physics I 3
PHY 195 Practical Physics II 2
Required Ancillary Course
COS 101 Introduction to Computer Science 2
General Study Courses
GSP 101 Communication in English I 2
GSP 111 The Use of Library and Study Skills 2
Elective Courses
Minimum of 2 units from the following: 2
CHM 101 Basic Principles of Chemistry I 2
CHM 171 Basic Practical Chemistry 2
STA 111 Probability I 2
STA 131 Inference I 2
Total Units 19
Second Semester
Major Courses
MTH 122 Elementary Mathematics III 3
PHY 122 Fundamental of Physics II 3
PHY 124 Fundamental of Physics III 3
General Study Courses
GSP 102 Communication in English II 2
Elective Course
Any 6 units from the following: 6
CHM 112 Basic Principle of Physical Chemistry 2
CHM 122 Basic Principle of Organic Chemistry 2
PHY 196 Practical Physics III 2
STA 112 Probability II 2
STA 132 Inference II 2
17
Second Year MATHEMATICS/PHYSICS
First Semester
Major Courses
MTH 211 Set, Logic and Algebra 3
MTH 215 Linear Algebra I 2
MTH 221 Real Analysis I 3
PHY 211 Structure of Matter 3
PHY 221 Mechanics 2
PHY 251 Electromagnetism 2
General Study Courses
GSP 201 Basic Concepts &Theory of Peace 2
GSP 207 Logic, Philosophy and Human Existence 2
Total Units 19
Second Semester
Major Courses
MTH 216 Linear Algebra II 2
MTH 222 Elementary Differential Equations I 3
MTH 224 Introduction to Numerical Analysis 3
PHY 241 Waves 3
PHY 261 Introduction to Atomic and Nuclear Physics 3
PHY 291 Practical Physics III 2
General Study Courses
GSP 202 Issues in Peace and Conflict Resolution 2
GSP 208 Nigerian People and Culture 2
Total Units 20
Third Year MATHEMATICS/PHYSICS
First Semester
Major Courses
MTH 311 Abstract Algebra I 3
MTH 321 Metric Space Topology 3
MTH 323 Complex Analysis I 3
PHY 301 Methods of Theoretical Physics I 2
PHY 321 Relativity Physics I 2
PHY 331 Thermal Physics 3
PHY 351 Electronics 2
PHY 391 Practical Physics V 2
Total Units 20
Second Semester
Major Courses
MTH 242 Mathematical Methods I 3
MTH 312 Abstract Algebra II 3
MTH 324 Vector and Tensor Analysis 3
MTH 326 Real Analysis II 3
PHY 302 Methods of Theoretical Physics I 2
PHY 362 Quantum Mechanics I 3
PHY 392 Practical Physics VI 2
Total Units 19
Fourth Year MATHEMATICS/PHYSICS
First Semester
Major Courses
MTH 315 Differential Geometry 3
MTH 327 Elementary Differential Equations II 3
*MTH 441 Mathematical Methods II 3
PHY 401 Computational Physics 2
PHY 421 Analytic Dynamics 3
PHY 451 Electromagnetic Theory 2
PHY 461 Quantum Mechanics II 2
18
SECOd Semester  
Major Courses  
MTH 328 Complex Analysis II 3
MTH 335 Dynamics of a Rigid Body 3
PHY 411 Solid State Physics 3
PHY 431 Statistical Physics 2
MTH/PHY 452/493 Project 4
Total Units 15

 

First Year MATHEMATICS/STATISTICS
First Semester
Major Courses
MTH 111 Elementary Mathematics I 3
MTH 121 Elementary Mathematics II 3
STA 111 Probability I 2
STA 131 Inference I 2
Required Ancillary Course
COS 101 Introduction to Computer Science 2
General Study Courses
GSP 101 Communication in English I 2
GSP 111 The Use of Library and Study Skills 2
Elective Course
Any 2-3 units from the following: 4/5
PHY 115 General Physics for Physical Science I 2
PHY 191 Practical Physics I 2
CHM 101 Basic Principles of Chemistry I 2
CHM 171 Basic Practical Chemistry 2
ECO 101 Principles of Economics I 2
GLG 111 Physical Geology 2
18/19
Second Semester
MTH 122 Elementary Mathematics III 3
STA 132 Inference II 2
STA 172 Statistical Computing I 2
General Study Courses
GSP 102 Communication in English II 2
Elective Course
Any 6-7 units from the following: 6/7
ECO 102 Principles of Economics II 2
CHM 112 Basic Principle of Physical Chemistry 2
PHY 116 General Physics for Physical Science II 2
CHM 122 Basic Principle of Organic Chemistry 2
GLG 142 Earth History 3
15/16
Second Year MATHEMATICS/STATISTICS
First Semester
Major Courses
MTH 211 Set, Logic and Algebra 3
MTH 215 Linear Algebra I 2
MTH 221 Real Analysis I 3
STA 211 Probability III 2
STA 231 Inference III 2
Required Ancillary Courses
COS 201 Introduction to Computer Systems 3
General Study Courses
GSP 201 Basic Concepts &Theory of Peace 2
GSP 207 Logic, Philosophy and Human Existence 2
     19
Second Semester
Major Courses
MTH 216 Linear Algebra II 2
MTH 222 Elementary Differential Equations I 3
MTH 224 Introduction to Numerical Analysis 3
STA 212 Probability IV 2
STA 232 Inference IV 2
STA 272 Statistical Computing I 2
General Study Courses
GSP 202 Issues in Peace and Conflict Resolution 2
GSP 208 Nigerian People and Culture 2
18
Third Year MATHEMATICS/STATISTICS
First Semester
Major Courses
MTH 321 Metric Space Topology 3
MTH 327 Elementary Differential Equation II 3
MTH 331 Introduction to Mathematical Modelling 3
STA 321 Distribution Theory 2
STA 331 Inference V 2
STA 341 Sampling Theory and Survey Methods I 2
STA 363 Operation Research I 3
Required Ancillary Courses
COS 201 Computer Programming I 2
20
Second Semester
Major Courses
MTH 324 Vector and Tensor Analysis 3
MTH 326 Real Analysis II 3
MTH 336 Dynamics of Rigid Body 3
STA 323 Analysis of Variance I 2
STA 332 Inference VI 2
STA 342 Sampling Theory and Survey Methods II 2
STA 362 Operation Research II 2
16/17
Fourth Year MATHEMATICS/STATISTICS
First Semester
Major Courses
MTH 323 Complex Analysis I 3
MTH 337 Optimization Theory I 2
MTH 421 Ordinary Differential Equation 3
MTH 441 Mathematical Methods II 3
STA 421 Design and Analysis of Experiment I 2
STA 461 Operation Research II 2
Elective Courses      
Minimum of 4-5 units from the following: 4/5
STA 413 Stochastic Process I 2
STA 415 Time Series I 2
STA 431 Bayesian Inference I 2
STA 435 Nonparametric Methods I 2
STA 433 Multivariate Analysis I 2
MTH 429 Functional Analysis 3
Total Units 19/20
Second Semester  
Major Courses  
MTH 328 Complex Analysis II 3
MTH 338 Optimization Theory II 2
MTH 428 Partial Differential Equations 3
MTH/STA 452/492 Project 4
Elective Courses  
Minimum of 4 units from the Following: 6/7
STA 414 Stochastic Process II 2
STA 416 Time Series II 2
STA 424 Design and Analysis of Experiment II 2
STA 432 Bayesian Inference II 2
STA 436 Nonparametric Methods II 2
STA 434 Multivariate Analysis II 2
STA 462 Operation Research III 2
16

 

DESCRIPTION OF COURSES

MTH 111        Elementary Mathematics I                                             3 units

Elementary Set theory, subsets, union, intersection, complements. Venn diagrams, Real numbers, integers, rational and irrational numbers, mathematical induction, real sequences and series, theory of quadratic equations, binomial theorem. Circular measure, trigonometric functions of angles of any magnitude, addition and factor formulae. Complex numbers, algebra of complex numbers, the Argand Diagram, De Moivre’s theorem, nth roots of unity.

MTH 121        Elementary Mathematics II                                           3 units

Functions of a real variable, graphs, limits and continuity. The derivative as limit of rate of change. Techniques of differentiation. Curve sketching, integration as an inverse of differentiation. Methods of integration, definite integrals. Application of integration to areas and volumes.

MTH 122        Elementary Mathematics III                                         3 units

Geometric representation of vectors in 1-3 dimensions, Components, direction cosines. Addition of vectors and multiplication of vectors by a scalar, linear independence. Scalar and vector products of two vectors. Differentiation and integration of vectors with respect to a scalar variable. Two-dimensional coordinate geometry. Straight lines, circles, parabolas, ellipses, hyperbolas. Tangents and normals. Kinematics of a particle. Components of velocity and acceleration of a particle moving in a plane. Force and momentum. Newton’s laws of motion; motion under gravity, projectile motion, resisted vertical motion of a particle, elastic string, motion of a simple pendulum, impulse and change of momentum. Impact of two smooth elastic spheres. Direct and oblique impacts.

MTH 132        Elementary Mechanics I                                                 3 units

Vectors: Algebra of vectors; coplanar forces; their resolution into components, equilibrium conditions, moments and couples, parallel forces; friction; centroids and centres of gravity of particles and rigid bodies; equivalence of sets of coplanar forces. Kinematics and rectilinear motion of a particle, vertical motion under gravity, projection, relative motion. Dynamics of a particle. Newton’s laws of motion; motion of connected particles.

MTH 201        Advanced Mathematics I                                                3 units

Mathematics and symbolic logic: inductive and deductive systems. Concepts of sets;

mappings and transformations. Introduction to complex numbers. Introduction to vectors, Matrices and determinants.

MTH 202        Advanced Mathematics II                                             3 units

Discrete and continuous variables. The equation of a straight line in various forms. The circle. Trigonometric functions; logarithmic functions; exponential functions. Maxima, minima and points of inflexion. Integral Calculus: Integration by substitution and by parts. Expansion of algebraic functions. Simple sequences and series.

MTH 203 Advanced Mathematics III                                                  3 units

Matrices and determinants, introduction to linear programming and integer programming, sequences and series. Taylor’s and Maclaurin’s series. Vector Calculus, line integrals and surfce integrals. Gauss’ (divergence), Green’s and Stokes’ Theorems. Complex numbers and functions of a complex variable; conformal mapping; infinite series in the complex plane.

MTH 204        Advanced Mathematics IV                                            3 units

Translation and rotation of axes, space curves; applications of vector Calculus to space curves; the Gaussian and Mean curvatures, the geodesic and geodesic curvature. Differential equations: sECOd order ordinary differential equations and methods of solutions. Partial differential equations: sECOd order partial differential equations and methods of solution.

MTH 205        Advanced Mathematics V                                              3 units

Translation and rotation of axes, plane geometry of lines, circles and other simple curves; lines in space; equations of the plane, space curve. The Gaussian and mean curvatures; the geodesic and geodesic curvature.

MTH 206        Advanced Mathematics VI                                            2 units

Complex analysis – Elements of the algebra of complex variables, trigonometric, exponential and logarithmic functions. The number system; sequences and series. Vector differentiation and integration.

MTH 207        Advanced Mathematics VII                                           2 units

Elements of linear algebra. Calculus: Elementary differentiation and relevant theorems. Differential equations: Exact equations, methods of solution of sECOd-order ordinary differential equations; partial differential equations, with applications.

MTH 208        Advanced Mathematics VIII                                        2 units

Numerical analysis: Linear equations, non-linear equations; finite difference operators. Introduction to linear programming.

MTH 211        Sets, Logic and Algebra                                                   3 units

Introduction to the language and concepts of modern mathematics; topics include: Basic set theory, mappings, relations, equivalence and other relations, Cartesian product. Binary logic, methods of proof. Binary operations, algebraic structures, semi-groups, rings, integral domains, fields. Homomorphism. Number systems; properties of integers, rationals, real and complex numbers.

MTH 215        Linear Algebra I                                                                2 units

System of linear equations. Matrices and algebra of matrices. Vector spaces over the real field. Subspaces, linear independence, bases and dimensions.Gram-Schmidt orthogonalization procedure. Linear transformations: range, null space and rank. Singular and non-singular transformations.

MTH   218      Three-Dimensional Analytic Geometry                  2 units

Plane curves, parametric representations, length of a plane arc, lines in three-space, surfaces,

cylinders, cylindrical and spherical coordinates, quadratic forms, quadrics and central quadrics.

MTH   216      Linear Algebra II                                                             2 units

Representations of linear transformations by matrices, change of bases, equivalence and similarity. Determinants. Eigenvalues and eigenvectors. Minimum and characteristic polynomials of a linear transformation. Cayley- Hamilton theorem, bilinear and quadratic forms, orthogonal diagonalization. Canonical forms.

MTH   221      Real Analysis I                                                                     3 units

Bounds of real numbers, convergence of sequences of numbers. Monotone convergence of series. Absolute and conditional convergence of series, and rearrangements. Completeness of reals and incompleteness of rationals. Continuity and differentiability of functions. Rolle’s and mean-value theorems for differentiable functions. Taylor series.

MTH 222        Elementary Differential Equations I                          3 units

First-order ordinary differential equations. Existence and uniqueness of solution. SECOd-order ordinary differential equations with constant coefficients. General theory of nth-order linear ordinary differential equations. The Laplace transform. Solution of initial- and boundary-value problems by Laplace transform method. Simple treatment of partial differential equations in two independent variables. Applications of ordinary and partial differential equations to physical, life and social sciences.

MTH 224        Introduction to Numerical Analysis                          3 units

Solution of algebraic and transcendental equations. Curve fitting, error analysis. Interpolation, approximation, zeros of non-linear equations of one variable. Systems of linear equations. Numerical differentiation and integration. Numerical solution of initial-value problems for ordinary differential equations.

MTH 231        Elementary Mechanics II                                                2 units

Impulse and Momentum, conservation of momentum; work, power and energy; work and energy principle, conservation of mechanical energy. Direct and oblique impact of elastic bodies. General motion of a particle in two dimensions, central orbits, motion in horizontal and vertical circles, simple harmonic motion, motion of a particle attached to a light inelastic spring or string. Motion of a rigid body about a fixed axis; moments of inertia

calculations; perpendicular and parallel axes theorems, principal axes of inertia and directions. Conservation of energy. Compound pendulum. Conservation of angular

momentum .

MTH 242        Mathematical Methods I                                                3 units

Real-valued functions of a real variable. Review of differentiation and integration and their applications. Mean-value theorem. Taylor series. Real-valued functions of two or three variables. Partial derivatives. Chain-rule, extrema, Lagrange’s multipliers, increments, differentials and linear approximations. Evaluation of line-integrals. Multiple integrals.

MTH 311        Abstract Algebra I                                                              3 units

Group: definition; examples, including permutation groups. Subgroups and cosets. Lagrange’s theorem and applications. Cyclic groups. Normal subgroups and quotient groups. Homomorphism, Isomorphism theorems. Cayley’s theorems. Direct products. Groups of small order. Group acting on sets. Sylow theorems,

MTH 312        Abstract Algebra II                                                            3 units

Rings: definition; examples, including Z, Zn; rings of polynomials and matrices, integral domains, fields, polynomial rings, factorization. Euclidean algorithm for polynomials, H.C. F. and L.C.M. of polynomials.ideals and quotient rings, P.I.D.’s, U.F.D’s, Euclidean rings. Irreducibility. Field theorems, degree of an extension, minimum polynomial. Algebraic and transcendental extensions. Straight-edge and compass constructions.

MTH 313        Geometry I                                                                           2 units

Coordinates in Â3. Polar coordinates; distance between points, surfaces and curves in space. The plane and straight line.

MTH 314        Geometry II                                                                         2 units

Introductory projective geometry. Affine and Euclidean geometries.

MTH   316      Differential Geometry                                                     3 units

Concept of a curve, regular, differentiable and smooth curves, osculating, rectifying and normal planes, tangent lines, curvature, torsion, Frenet-Serret formulae, fundamental, existence and uniqueness theorem, involutes, evolutes, spherical indicatrix, developable surfaces, ruled surfaces, curves on a surface, first and sECOd fundamental forms, lines of curvature, umbilics, asymptotic curves, geodesics. Topological properties of simple surfaces.

MTH 321        Metric Space Topology                                                     3 units

Sets, metrics and examples. Open spheres or balls. Open sets and neighbourhoods. Closed sets. Interior, exterior, frontier, limit points and closure of a set. Dense subsets and separable space. Convergence in metric space, homeomorphism. Continuity and compactness, connectedness.

MTH   327      Elements of Differential Equations II                       3 units

Series solution of sECOd-order differential equations. Sturm-Liouville problems. Orthogonal polynomials and functions. Fourier series, Fourier-Bessel and Fourier-Legendre series. Fourier transformation, solution of Laplace, wave and heat equations by the Fourier method. (separation of variables). Special functions:Gamma,Beta, Bessel, Legendre and Hypergeometric

MTH 323        Complex Analysis I                                                          3 units

Functions of a complex variable: limits and continuity of functions of a complex variable. Derivation of the Cauchy-Riemann equations; Bilinear transformations, conformal mapping, contour integrals. Cauchy’s theorem and its main consequences. Convergence of sequences and series of functions of a complex variable. Power series. Taylor series.

MTH 324        Vector and Tensor Analysis                                            3 units

Vector algebra. The dot and cross products. Equations of curves and surfaces. Vector differentiation and applications. Gradient, divergence and curl. Vector integrals: line, surface and volume integrals. Green’s, Stoke’s and divergence theorems. Tensor products of vector spaces. Tensor algebra. Symmetry. Cartesian tensors and applications.

MTH 326        Real Analysis II                                                                   3 units

Riemann integral of real function of a real variable, continuous monopositive functions. Functions of bounded variation. The Riemann-Stieltjes integral. Point-wise and uniform convergence of sequences and series of functions ®Â. Effects on limits (sums) when the functions are continuously differentiable or Riemann integrable power series.

MTH 328        Complex Analysis II                                                           3 units

Laurent expansions, isolated singularities and residues. The Residue theorem, calculus of residues and application to the 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 331        Introduction to Mathematical Modelling                   3 units

Methodology of model building; identification, formulation and solution of problems; cause-effect diagrams. Equation types. Algebraic, ordinary differential, partial differential, difference, integral and functional equations. Applications of mathematical models to physical, biological, social and behavioural sciences.

MTH 334        Special Theory of Relativity                                           4 units

Classical mechanics and principles of Relativity, Einstein Postulates; Interval between events, Lorentz transformation and its consequences; Four-Dimensional Space-time, Relativistic Mechanics of a particle, Maxwell’s theory in a Relativistic form. Optical phenomena.

MTH 335        Introduction to Operations Research                        3 unitsPhases of operations research study. Classification of operations research models; linear, dynamic and integer programming. Decision theory. Inventory models. Critical path analysis and project controls.

MTH 336        Dynamics of a Rigid body                                               3 units

General motion of a rigid body as a translation plus a rotation. Moment of inertia and product of inertia in three dimensions. Parallel and perpendicular axes theorems. Principal axes, angular momentum, kinetic energy of a rigid body. Impulsive motion. Examples involving one- and two-dimensional motion of a simple systems. Moving frames of reference; rotating and translating frames of reference. Coriolis force. Motion near the earth’s surface. The Foucauli’s pendulum. Euler’s dynamical equations of motion of a rigid body with one point fixed. The symmetric top. Precessional motion.

MTH 337        Optimization Theory II                                                   2 units

Linear programming models. The simplex method: formulation and theory, duality, integer programming; transportation problem. Two-person-zero-sum games. Nonlinear programming. Quadratic programming.

MTH 338        Optimization Theory II                                                  2 units

Kuhn-Tucker methods. Optimality criteria. Single variable optimization. Multivariable techniques. Gradient methods.

MTH 339        Analytic Dynamics                                                           3 units

Degrees of freedom. Holonomic and non-holonomic constraints. Generalized coordinates. Lagrange’s equations of motion for holonomic systems; force dependent on coordinates only; force obtainable from a potential. Impulsive force.

MTH   341      Discrete Mathematics I                                                   2 units

Groups and subgroups, group axioms, permutation groups, cosets, graphs, directed and undirected graphs, subgraphs, cycles, connectivity. Applications (flow charts) and state-transition graphs.

MTH 342        Discrete Mathematics II                                                 2 units

Lattices and Boolean algebra. Finite fields: Mini-polynomials, irreducible polynomials,

polynomial roots. Applications (error-correcting codes)

MTH 344       Numerical Analysis I                                                        3 units

Polynomials and splines approximation. Orthogonal polynomial and Chebysev approximation. Direct and iterative methods for the solution of system of Linear equations. Eigenvalue problem – power methods, inverse power method, pivoting strategies.

MTH 412        Abstract Algebra III                                                          3 units

Splitting fields. Separability. Algebraic closure. Solvable groups. Fundamental theorem of Galois theory. Solution by radicals. Definition and examples of modules, submodules and quotient modules. Isormorphism theorems. Theory of group representations.

MTH 421        Ordinary Differential Equations                                 3 units

Existence and uniqueness of solutions; dependence on initial conditions and on parameters, general theory for linear differential equations with constant coefficients. The two-point Sturm-Liouville boundary value problem; self-adjointness; Sturm theory; stability of solutions of nonlinear equations; phase-plane analysis. Floquet Theory. Integral equations classifications – Voltera and Freedhom types. Reduction of ordinary differential equations to integral equations.

MTH   424      General Topology                                                              3 units

Topological spaces, definition, open and closed sets, neighbourhood. Coarser and finer topologies. Bases and sub-bases. Separation axioms, compactness, local compactness, connectedness. Construction of new topological spaces from given ones. Subspaces, quotient spaces, continuous functions, homomorphisms, topological invariants, spaces of continuous functions. Point-wise and uniform convergence.

MTH 425        Lebesgue Measure and Integration                            3 units

Lebesgue measure: measurable and non-measurable sets. Measurable functions. Lebesgue integral: integration of non-negative functions, the general integral convergence theorems.

MTH 426        Measure Theory                                                                 4 units

Abstract Lp– spaces.

MTH 427        Field Theory in Mathematical Physics                      3 units

Gradient, divergence and curl. Further treatment and application of the definitions of the differential. The integral definition of gradient, divergence and curl. Line-, surface- and volume- integrals. Green’s, Gauss’s, and Stokes’ theorems. Curvilinear coordinates. Simple notion of tensors. The use of tensor notations.

MTH 428        Partial Differential Equations                                      3 units

Partial differential equations in two independent variables with constant coefficients: the Cauchy problem for the quasi-linear first- order partial differential equations in two independent variables; existence and uniqueness of solutions. The Cauchy problem for the linear, sECOd- order partial differential equation in two independent variables, existence and uniqueness of solution: normal forms. Boundary- and initial – value problems for hyperbolic, elliptic and parabolic partial differential equations.

MTH 429        Functional Analysis                                                           3 units

A survey of the classical theory of metric spaces, including Baire’s category theorem, compactness, separability, isometries and completion.; elements of Banach and Hilbert spaces; parallelogram law and polar identity in Hilbert space H; the natural embeddings of normed linear spaces into sECOd dual, and H onto H; properties of operators including the open mapping and closed graph theorem; the spaces C(X), the sequence (Banach) spaces, lpn, lp and (c=space of convergent sequences).

MTH 432        General Theory of Relativity                                          3 units

Particles in a gravitational field: Curvilinear coordinates, intervals. Covariant differentiation: Christoffel symbols and metric tensor. The constant gravitational field. Rotation. The curvature tensor. The action function for the gravitational field. The energy- momentum tensor. Newton’s laws. Motion in a centrally symmetric gravitational field. The energy- momentum pseudo- tensor. Gravitational waves. Gravitational fields at large distances from bodies. Isotropic space. Space- time metric in the closed and open isotropic models.

MTH 434        Elasticity                                                                                 3 units

Stress and strain analysis, constitutive relations, equilibrium and compatibility equations, principles of minimum potential and complementary energy, principles of virtual work, variational formulation, extension, bending and torsion of beams; elastic waves.

MTH 436        Fluid Dynamics                                                                     3 units

Real and ideal fluids; differentiation following the motion of fluid particles. Equations of motion and continuity for incompressible inviscid fluids. Velocity potentials and Stokes’ stream function. Bernoulli’s equation with applications to flows along curved paths. Kinetic energy. Sources, sinks and doublets in 2- and 3- dimensional flows; limiting stream lines. Images and rigid planes, streaming motion past bodies including aerofoils.

MTH 437        Systems Theory                                                                     4 units

Existence, boundedness and periodicity for solutions of linear systems of differential equations with constant coefficients. Lyapunov theorems. Solution of Lyapunov stability equations. ATP+PA=Q. Controllability and observability. Theorems on existence of solution of linear systems of differential equations with constant coefficients.

MTH 438        Electromagnetism                                                               3 units

Maxwell’s field equations. Electromagnetic waves and electromagnetic theory of light; plane electromagnetic waves in non- conducting media; reflected and refractional place- boundary. Wave- guides and resonant cavities. Simple radiating systems. The Lorentz-Einstein transformation. Energy and momentum. Electromagnetic 4- vectors. Transformation of (E.H.) fields. The Lorentz force.

MTH 439        Analytical Dynamics II                                                       3 units

Lagrange’s equations for non- holonomic systems. Lagrange’s multipliers. Variational principles. Calculus of variations. Hamilton’s principle. Lagrange’s equations of motion from Hamilton’s principle. Contact or canonical transformations. Normal modes of vibration. Hamilton- Jacobi equations for a dynamical system.

MTH 441        Mathematical Method II                                                      3 units

Calculus of variations: Lagrange’s functional and associated density. Necessary condition for a weak relative extremum. Hamilton’s principle. Lagrange’s equations and geodesic problems. The Du Bois Raymond equation and corner conditions. Variable end points and related theorems. Sufficient conditions for a minimum, isoperimetric problems. Variational integral transforms. Laplace, Fourier and Hankel transforms. Complex variable methods; convolution theorems; applications to solutions of differential equations with initial/boundary conditions.