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 R^{N} | 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, Z_{n}; 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 Â^{3}. 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®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 L_{p}– 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, l_{p}^{n}, l_{p} 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.
DEPARTMENT OF MATHEMATICS
POSTGRADUATE PROGRAMMES
IN PURE AND APPLIED
MATHEMATICS
DEPARTMENT OF MATHEMATICS
POSTGRADUATE PROGRAMMES IN PURE AND APPLIED MATHMATICS
PHILOSOPHY
It is becoming very obvious that Mathematics is the arrowhead of development not only in the Science- engineering sciences, physical sciences, social sciences, medical sciences- but indeed in all facets of the economy of any nation. Thus the postgraduate programme in mathematics is designed to provide training in the theory and application of mathematics in every area of human endeavour and stimulate creative thinking and research in every methods and solution of real life problems.
LISTS OF APPROVED SUPERVISORS
PROFESSORS
Amazigo, J.C. (FAS) B.Sc. (RPI), M.Sc., Ph. D (Harvard) Applied Mathematics
Chidume, C.E. (FAS) B.Sc. (Nigeria), M.Sc. (Queens), Ph. D (Ohio State) Nonlinear Operator Theory
Eke, A.N. B.Sc., M.Sc., Ph. D (Nigeria) Control Theory
Osilike, M.O. B.Sc., M.Sc., Ph. D (Nigeria), DICTP (Trieste) Nonlinear Operator Theory
Oyesanya, M.O. B.Sc., M.Sc., Ph. D (Nigeria) Applied Mathematics
Ochor, F.I. B.Sc., M.Sc. (Nigeria), M.Phil, Ph. D (SISSA) Differential Equations
Mbah, G.C.E B.Sc., M.Sc. (BENIN), Ph. D (Nigeria) Modelling
SENIOR LECTURERS
Obi, E.C. B.Sc. (I.C. Portland), M.Sc., Ph. D (Toledo) Summability Theory
LECTURER I
Shehu, Y. B.Sc. (Ladoke Akintola), M.Sc. (Nigeria), Ph. D (AUST) Functional Analysis
DEPARTMENT OF MATHEMATICS
POSTGRADUATE DIPLOMA (PGD) IN MATHEMATICS
POST GRADUATE Diploma (PGD) IN MATHEMATICS
The PGD program in mathematics is designed to cater for graduates of other Departments in Physical Sciences, Engineering, Mathematics Education and mathematically related disciplines who may want to pursue higher degrees in Mathematics. The PGD program is NOT meant for graduates of Mathematics with Third Class.
OBJECTIVES:
The main objectives of the PGD programme is to open the door of the universal language of mathematics to non- mathematics graduates to enter into productive field of science and technology, communication and information technology, financial mathematics, and give to those interested and qualified a solid background in mathematics for higher degrees and scientific breakthroughs.
ADMISSION REQUIREMENTS
Candidates for the PGD must possess a first degree in related disciplines as noted above with a CGPA of not less than 2.5/5.0 in addition to General Certificate of Education (GCE) O/L with five credits including English Language, Mathematics, Physics and any other two physical science subjects.
FIRST SEMESTER.
- MTH 511 ANALYTICAL DYNAMICS 3
- MTH 521 NUMERICAL ANALYSIS 3
- MTH 531 FINANCIAL MATHEMATICS 3
- MTH 541 REAL ANALYSIS 3
- MTH 551 ABSTRACT ALGEBRA 3
- MTH 561 PARTIAL DIFFERENTIAL EQUATION 3
- MTH 571 MATHEMATICAL METHODS 3
- MTH 581 MEASURE AND INTEGRATION 3
SECOND SEMESTER
- MTH 512 COMPLEX ANALYSIS 3
- MTH 522 ORDINARY DIFFERENTIAL EUATIONS 3
- MTH 532 TOPOLOGY 3
- MTH 542 FUNCTIONAL ANALYSIS 3
- MTH 552 ADVANCED CALCULUS 3
- MTH 562 MATHEMATICAL MODELING 3
- MTH 567 OPERATION RESEARCH 3
- MTH 582 CONTROL THEORY 3
- MTH 592 BANACH ALGEBRA AND SPECTRAL THEORY 3
Minimum of 15 units to be taken
Total=30units
Project=4 units to be taken DURING first semester to the students and examined at the end of the second semester.
COURSE CONTENTS
MTH 592 BANCH ALGEBRAS AND SPECTRAL THEORY
A brief review of Banach Space Theory .Basic of Banach Algebras. The functional Calculus. The spectrum. Commutative Banach Algebra. Bounded Operators on Hilbert Space, Unbounded Operators. The Spectral Theory of Operators C^{A}-Algebras and Von Neumann Algebras.
MTH 542 FUNCTIONAL ANALYSIS
Normed Linear Spaces. An introduction to Operators Hilbert Space. Topological Vector Spaces. The Hahn-Banach Theorem. Weak Topologies and Dual Spaces. Local Compactness and External Points. Operator Theory.
MTH 551 ABSTRACT ALGEBRA
Basic Axioms and Examples of Groups Subgroups and Lattice of Subgroups. Quotient Groups and Homomorphisms.P-group Nilpotent Groups and Solvable Groups. Definition of Ring. Ring Homomorphism and Quotient Rings. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains. Polynomial Rings .Review of Field Theory and Galois Theory.
MTH 532 GENERAL TOPOLOGY
Brief Review of Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem.Metrization Theorem and Paracompactness. Complete Metric Spaces and Function Spaces.Baire Space and Dimension Theory.
MTH 552 ADVANCE CALCULUS
Function of Several Variables. Functions from R^{n }to R^{n}.Partial Derivatives.Jacobian.Inverse Function Theorem. Implicit Function Theorem.
MTH 561 PARTIAL DIFFERENTIAL EQUATIONS
Basic examples of linear partial differential equations, their fundamental equations and solutions. The Cauchy problem for the linear second order partial differential equations in two independent variables: existence and uniqueness of solutions; normal forms. Riemann method. Hyperbolic, elliptic and parabolic partial differential equations. Boundary value and mixed boundary value problems.
MTH 541 REAL ANALYSIS
Review of: The Concept of upper and lower limits of bounded sequences. Category Spaces, the Bairew Category Lemma, the Unit Open Ball Lemma, Zorn’s Lemma, Basic Properties of Hilbert Space and Banach Spaces. Theory of Functions of a Real Variable. Lebesgue Measure and Integral. Differentiation and Integration.
MTH 581 MEASURE AND INTEGRATION
Basic Definitions and Examples. Measures and Outer Measures. Extensions of Measures. Measurable Functions. Integration. General Set Functions.
MTH 511 ANALYTICAL DYNAMICS (3)
Motion of rigid bodies. Generalized coordinates conservative fields. Degrees of freedom. Holonomic and non-holonomic systems. Languages equation for holonomics systems, force dependent coordinates only, force obtainable from a potential. Hamilton’s equation, Impulsive motion, Small oscillative. Normal modes, Three-dimensional motion. Eulerian angles, spinning tops, gyrostats, rolling bodies and frames of reference. Calculus of variation.
MTH 521 NUMERICAL ANALYSIS
Numerical differentiatives and integration by varios methods. Guassina quadratine. Numerical method for ordinary and partial differential equations. Boundary value problems. Computation of eigenvalues of symmetric matrices. Finite, Difference methods, equations and operatives. Discrete variable methods for sulutions of IVPS ordinary differential equations. Discrete and continuous Tan methods for solving IVP-ODES, error analysis.
MTH 531- FINANCIAL MATHEMATICS (3)
Measures of central tendency, retives and correlative. Distribution theories and types of distributives. Stocks and shares. Risks analysis of stock and shares. Investments and returns on investments. Portfolio selection. Optimizing returns on portfolios selection.
MTH 571- MATHEMATICAL METHODS
Gradient, divergence and curl of vectors. The integral definition of gradient, divergence and curl of vectors curvilinear coordinates. Simple notion of tensors. Calculus of variation; Lagrange’s functional and associated density. Conditions for strong and relative extremum. Geodesic problems. Variable end point theorems and related theorems. Isoperimetric problems. Variational integral transforms: Laplace, Fourier, Hankel and Mellen transforms. Complex variable methods, convolution theorem and applications to solutions of IVP/BVP ODES. Series solutions of second order equation about ordinary and regular singular points: application.
MTH 562 MATHEMATICAL MODELLING
Methodology of model building. System study and abstractions of relevant information for mathematical formulations of the required equations. Various types of mathematical model formulation: Descrete, Stochastic, Differential, Integra-differential, algebraic difference etc. application of the art of mathematical modelling to; environmental studies, economy, physical, biological, drug Kinetics, Chemical reactions. Simulations and interpretation of model results.
MTH 572: OPERATION RESEARCH (3)
Inventory problem; graph and networks; stock control; quelling problems. Decision theory. Non-linear programming algorithms and their reliability. Scheduling. Special types of linear programming problems. The dual simplex method. Advanced topics in Mathematical programming. Dynamics programming. Game theory. Integer and mixed programming.
MTH 582 CONTROL THEORY
Existence, boundedness and periodicity for solutions of linear systems of differential equations with content coefficients. Stability theorems and analysis for differential equations: Lyapuno and other methods. Sets: reachable sets, attainable sets. Dynamical systems in the space. Reachability, stabilizability and detectability. Equivalence of controllability and pole assignability.
MTH 512 COMPLEX ANALYSIS
Analytic functions and conformal mappings. Analytic contimatives and elementary Reimann surfaces. Transformations, infinite products; entire functions: include order and types. The product theorems of Weierstrass and others; the Riemann mapping theorems.
MAT 506 Group Representation Theory 3 Credit Units
Representation of groups by linear transformations; group algebras, character theory and modular representations. Representation theory of algebraic groups, representation of finite groups; representation of compact and locally compact groups; representation of Lie groups. Unitary representation theory.
DEPARTMENT OF MATHEMATICS
MASTERS (M.Sc.) DEGREE PROGRAMME
MASTER’S (M.Sc) DEGREE PROGRAMME
The department offers Academic Master’s Degree and Doctor of Philosophy (Ph.D) Programmes in Pure and Applied Mathematics with specialization in the following areas: Topology, Real Analysis, Functional Analysis, Differential Equations, Continuum Mechanics, Solid Mechanics, Fluid Mechanics, Modelling, Optimization, Control Theory, Operator Theory and Summability Theory.
ADMISSION REQUIREMENT FOR MASTER’S PROGRAMME
- Candidates with Bachelor’s degree from approved university must obtain a minimum of second class lower division with CGPA of 2.5/5.0
- All candidates must have five credit passes including English Language, Mathematics and two relevant science subjects at O’Level preferably Physics and Chemistry or Biology or Geography.
MODE OF STUDY:
The Academic Master’s degree shall be for four semesters by coursework and project report or by coursework and research dissertation for full time students and six semesters for part-time students. Every Master’s degree student shall take 24 credit units from the core course INCLUDING general courses, project/dissertation and seminar AND 6 credit units from the elective courses relevant to area of specialization.
CORE COURSES
- MTH 800/MTH 561 Research Project/Dissertation 6 Credit Units
- MTH 802 Topology 3 Credit Units
- MTH 803 Real Analysis 3 Credit Units
- MTH 804 Complex Analysis 3 Credit Units
- MTH 805 Partial Differential Equations 3 Credit Units
- MTH 807 Advanced Methods of Applied Maths. 3 Credit Units
- MTH 806 Asymptotic Method 3 Credit Units
- MTH 808 Geometry of Branch Space 3 Credit Units
- MTH 824 Seminar 2 Credit Units
REQUIRED GENERAL CORE COURSES
- PGC 601 ICT and Research Methodology 3 Credit Units
ELECTIVE COURSE
The M .Sc. Student in addition to the above specified core course must take 6 Credit Units from the
Following elective courses:
(A) PURE MATHEMATICS OPTION
MAT 801 Algebra 3 Credit Units
MAT 809 Group Representation theory 3 Credit Units
MAT 810 Number Theory 3 Credit Units
MAT 811 Category Theory 3 Credit Units
MAT 812 Lie Groups 3 Credit Units
MAT 813 Differential Manifold 3 Credit Units
MAT 815 Integral Equations 3 Credit Units
MAT 816 Theory of Distributions 3 Credit Units
MAT 817 Introduction to Mathematical Modelling 3 Credit Un
(B) APPLIE MATHEMATCS OPTION
MAT 818 Quantum Mechanics 3 Credit Units
MAT 819 Fluid Mechanics 3 Credit Units
MAT 820 Elasticity 3 Credit Units
MAT 821 Electromagnetic Theory 3 Credit Units
MAT 822 Visco- Elasticity and Plasticity 3 Credit Units
MAT 823 Control Theory 3 Credit Units
MAT 824 Finite Element Methods 3 Credit Units
MAT 825 Biomathematics 3 Credit Units
MAT 827 Fractional Calculus and Applications 3 Credit Units
DEPARTMENT OF MATHEMATICS
DOCTORAL (Ph.D.) DEGREE PROGRAMME
DOCTORAL (Ph.D) PROGRAMME
ADMISSION REQUIREMENT FOR DOCTORAL PROGRAMME
- Candidates with Bachelor’s degrees from approved university must obtain a minimum second class lower division with a CGPA OF 2.5/5.0
- All candidates must have five credit passes including English, Mathematics and two relevant science subjects at O’Level preferably Physics and Chemistry or Biology or Geopraphy.
- Candidates must have Academic Master’s degree in Mathematics in relevant are with CGPA of 4.0/5.0 and thesis score not lower than 60%.
- Candidates must demonstrate adequate intellectual capacity, maturity and effective decision making and problem solving potentials.
OBJECTIVES:
Our postgraduate programmes have the following objectives:
- Production of high calibre mathematicians equipped to man leadership positions in academia, industries, research centres where a sound knowledge of mathematics and mathematical thinking and skills are required particularly in a burgeoning economy like ours.
- Training a crop of mathematicians that can give incisive breakthroughs in understanding, and modelling of epidemiological diseases, engineering structures, and cncise development and progression in modern day diseases like cancer, diabetes, high blood pressure etc.
- Training people that can stand with their heads high up engaging in cutting edge research in mathematics.
MODE OF STUDY:
The doctoral Ph.D shall be for six semesters (minimum) and ten semesters (maximum) by coursework and research thesis. Every doctoral student shall take 30 credit units INCLUDING thesis of 12 Credit Units, seminar 6 units and 12 credit units of taught courses consisting of 6 credit units from departmental courses and 6 credit units from PG School organized courses namely
PGC701 Synopsis and Grant writing 3 Credit Unit
ELECTIVE COURSES
The Ph. D Students in addition to the above specified core course must take 6 Credit Units from the following elective courses:
(C) PURE MATHEMATICS OPTION
MAT 801 Algebra 3 Credit Units
MAT 809 Group Representation theory 3 Credit Units
MAT 810 Number Theory 3 Credit Units
MAT 811 Category Theory 3 Credit Units
MAT 812 Lie Groups 3 Credit Units
MAT 813 Differential Manifold 3 Credit Units
MAT 814 Theory of Integration 3 Credit Units
MAT 815 Integral Equations 3 Credit Units
MAT 816 Theory of Distributions 3 Credit Units
MAT 817 Introduction to Mathematical Modelling 3 Credit Units
(D) APPLIED MATHEMATIC OPTION
MAT 818 Quantum Mechanics 3 Credit Units
MAT 819 Fluid Mechanics 3 Credit Units
MAT 820 Elasticity 3 Credit Units
MAT 821 Electromagnetic Theory 3 Credit Units
MAT 822 Visco-Elasticity and Plasticity 3 Credit Units
MAT 823 Control Theory 3 Credit Units
MAT 824 Finite Element Methods 3 Credit Units
MAT 825 Biomathematics 3 Credit Units
MAT 827 Fractional Calculus and Applications 3 Credit Units
DISCRIPTION OF COURSES
PGC 701 Synopses and Grant Writing 3 Credit Units
Identification of types and nature of grants and grant writing: mining of grants application calls on the internet. Determining appropriate strategy for each grant application. Study of various grant application structures and contents and writing of concept notes, detailed project description, bugeting and budget defence. Study of simple grant writings in various forms and writing of mock research and other grants. Identification of University of Nigeria synopsis structure and requirements (Introduction, Methodology and Results).Determining the content of each sub-unit of the synopsis. Steps in writing the synopsis from the Dissertation/Thesis document. Structural and language issues. Common errors in synopsis writing and strategies for avoiding them. The roles of the students and supervisors in the production of a synopsis. Writing of mock synopsis. All registered Ph. D students must attend a solution-based interactive Workshop to be organized by the school of postgraduate studies for a practical demonstration and application of the knowledge acquired from the course conducted by selected experts.
MTH 801 Algebra 3 Credit Units
Sylow theorems, direct products, fundamental theorem of finite Abelian groups, fields of quotient, Euclidean rings, polynomial rings over commutative rings, inner product spaces, theory modules, sub-modules, quotient modules, module over principal ideal domains. Application of finitely generated Abelian group field extension fields elements of Galois Theory, solvability radicals.
MTH 802 Topology 3 Credit Units
Review of categories and functions. Homology, fundamental group, covering transformation, simplicial complexes. Singular homology. Universal co-efficient theorem for homology and cohomology. Spectral sequence.
MTH 803 Real Analysis 3 Credit Units
Measures and integration. Outer measure, Lebesgue Measure. Basic properties of Banach and Hilbert Spaces. Operators, Duality. Basic theorems in functional analysis. Classical Banach Spaces. Spectral theory of operators in Hilbert spaces. L2 space as a Hilbert space. Banach Algebras. Gelfand theory, compact operators. Examples and applications to classical analysis.
MTH 804 Complex Analysis 3 Credit Units
Periodic functions, Weierstrass functions, elliptic curves. Modular forms. Algebraic functions, Riemann surfaces. Covering surfaces, covering transformations. Discontinuous groups of linear transforms, automorphic forms.
MTH 805 Partial Differential Equations 1 3 Credit Units
Basic examples of linear partial differential equations, their fundamental equations, and their fundamental solutions. Existence and regularity of solutions (Local or Global) of the Cauchy problems; boundary value problems and mixed boundary value problems. The fundamental solutions of their partial difference equations.
MTH 807 Advanced Methods of Applied Maths 3 Credit Units
The emphasis will be on advanced methods of solution rather tan theory of ordinary and partial Differential equations. Power and product series and special functions, contour integral representation, integral transforms, conformal mapping. Wiener-Hopf techniques.
MTH 806 Asymptotic Method 3 Credit Units
Asymptotic sequences and series, operations on asymptotic series, asymptotic evaluation of functions defined by contour integral including methods of stationary phase and steepest descant, uniform asymptotic expansion, asymptotic solutions of ordinary and partial differential equations, WKB approximations, singular perturbation.
MTH 808 Geometry of Banach Space 3 Credit Units
Uniform convex spaces and their characteristics inequalities. Strictly convex spaces, The Modulus of Convexity. Uniformly Smooth Banach Spaces and their Characteristics inequalities, the Modulus of Smoothness, Fretchet and Gateaux Differentiability. Duality Maps. Some Applications.
MTH 809 Group Representation Theory 3 Credit Units
Representations of groups by linear transformations; group algebras, character theory and modular representations. Representation theory of algebraic groups; representation of finite groups; representation of compact and locally compact groups; representation of Lie groups. Unitary representation theory.
MTH 810 Number Theory 3 Credit Units
Algebraic integers. Completions, the different and discriminant. Cyclotomic fields. Parallelotopes. Class- Number. Ideles and Adeles. Elementary properties of Zeta-functions. L-functions.
MTH 811 Category Theory 3 Credit Units
Categories, functions natural-transformation. Functor categories, limits. Products and coproducts. Pushbacks and Pushouts, adjoining functors. Normal and exact categories: Abelian categories, quotient categories.
MTH 812 Lie Groups 3 Credit Units
Lie groups and their Lie algebras, subgroups. Matrix groups: One-parameter groups, exponential map, Campbell-Hausdorff formula, Lie algebra of a matrix group, integration on matrix groups. Abstract Lie group.
MTH 813 Differentiable Manifolds 3 Credit Units
General manifolds. Topics such as smooth mappings, Immersions, submersions, transversality, intersection theory, vector fields of manifold; orientation of manifolds: Gaussian curvature, Riemannian manifolds, differential forms, integration on manifolds tensors and connections are included.
MTH 814 Theory of Integration 3 Credit Units
The theory on closed and bounded intervals: Gauges and integrals. Basic properties of the integral. The fundamental theorems of calculus. The Saks-Henstock Lemma. Measurable functions. Absolute integrability. Convergence theorems. Integrability and mean convergence. Measure, measurability and multipliers. Mode of convergences, substitution theorems. Applications. The theory of infinite intervals: General insight into intergration on infinite interval.
MTH 815 Integral Equations 3 Credit Units
Basic existence theorems: Equations with L2 kernels: Fredholm Theory; Nonlinear equations, Schauder Fixed-point theorem. Dual integral and series equations. Wiener_Hope equations and Technique. Singular integral equations. Applications.
MTH 816 Theory of Distributions 3 Credit Units
Topological vectors spaces and generalized functions; Distribution calculus and topology; convolution; Tempered distributions and their Fourtier transforms. Integral transforms of Mathematical Physics. Application.
MTH 817 Introduction to Mathematical Modelling 3 Credit Units
Mathematical modelling. The Art of transforming Real Life Situation into Mathematical statements. Examples will be drawn from Areas such as Biology, Business, Deformable Media, Industry and other dynamical system. Case studies.
MTH 818 Quantum Mechanics 1 3 Credit Units
Background of the axiomatic approach to Nul et al. axioms of continuum and Basic Concepts. Constitutive relations. Equations of Motions and other Equations of Motions and other Equations of Balance. The place of the Classical Theories.
MTH 819 Fluid Mechanics 3 Credit Units
Thermodynamics Compressive flow; waves; shocks; supersonic flow; Boundary Layer Theory; stability Turbulence.
MTH 820 Elasticity 3 Credit Units
Formulation of the Linear Theory; General Theorems; Plane Strain and generalized plane stress; Airy’s solution: Papkovich- Neuber representation; Basic singular solutions; Boundary- Value and Boundary initial value problem.
MTH 821 Electromagnetic Theory 3 Credit Units
Maxwell’s Equations; Electromagnetic Potentials: Tensor Calculus; Stress and Energy; Electro- Static and Magnetostatics, plane waves, cylindrical and spherical waves; Boundary Value Problems; Relativistic Kinematics and Lorentz Transformation: Electrodynamics.
MAT 822 Quantum Mechanics 11 3 Credit Units
Schrodinger equations; Stone’s Theeorem and its applications. Unitary transformations:
Heisenberg representation : Measurement: Quantum Theory of Scattering ;Angular Momentum.
Motion in external field; Base and Fermi Statistics: Perturbation Theory.
MAT 823 Visco-Elasticit And plasticity 3 Credit Units
Characteristics of various visco-elastic and Plastic material Basic equations .Boundary Value problems. Elastic-plastic problem.
MAT 824 Contro T herory 3 Credit Units
Dynamical System in the State Space. Reachability. Stabilizability and Detectability.
Equivalence of Controllability and Pole Assignability. The Calculus of Variations. Generalized Huygen’s principle. The Algebraic Riccati Equation. Lyapunov Stability. Applications to Economic Stabilization. Planning. Manpower Development. Resource Allocation under Constraints, etc Case Studies.
MAT 825 Finite Element Methods 3 Credit Units
Introduction to the Finite Element Method: Formulation of Finite Element Method using the principle and Virtual Displacement. General Isoparametri Formulation, and Variational Techniques. Generalization of the theorey. Application of the Finite Element Method to the solution of Engineering problems e.g. In Solid Mechanics. Heat Transfer. Fluid Dynamics and Mass Transfer. Development of
Appropriate Computer programme. Case Studies.
MAT 826 Biomathematics 3 Credit Units
Mathematical Methods of Deterministic or Stochastic aspects of Biological Systems e.g., Population dynamics, species interaction malaria epidemic, etc.
MAT 827 Fractional Calculus and Applications 3 Credit Units
Preliminaries –function spaces, continuity ,special functions of the fractional calculus –gamma functions, Mittag- Leffler functions; fractional integrals and fractional derivatives ;fractional differential equations ;methods of solving FDEs-Laplace transforms methods, fractional Green’s function ; Applications of models in engineering,-Physics, Fluid flows, Cancer and epidemiology.