FUPRE Mathematics Syllabus
FEDERAL UNIVERSITY OF PETROLEUM RESOURCES, EFFURUN
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE
CURRICULUM FOR B. SC. (HONS) IN MATHEMATICS
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Code
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Description
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Status
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Unit
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Semester
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Level
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1
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MTH
111
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GENERAL
MATHEMATICS 1
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C
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3
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First
Semester
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100L
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2
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GSE
112
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USE OF
LIBRARY
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C
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1
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First
Semester
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100L
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3
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GSE
111
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COMMUNICATION
IN ENGLISH1
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C
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2
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First
Semester
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100L
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4
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BIO
119
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PRACTICAL
BIOLOGY
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C
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1
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First
Semester
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100L
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5
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BIO
111
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GENERAL
BIOLOGY1
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C
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3
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First
Semester
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100L
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6
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CHM
112
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GENERAL
PHYSICAL CHEMISTRY
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C
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3
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First
Semester
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100L
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7
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PHY
119
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EXPERIMENTAL
PHYSICS1
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C
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1
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First
Semester
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100L
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8
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PHY
111
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GENERAL
PHYSICS1
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C
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3
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First
Semester
|
100L
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9
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CSC
111
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INTRODUCTION
TO COMPUTER SCIENCE
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C
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3
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First
Semester
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100L
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10
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MTH
112
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DATA
ANALYSIS
|
R
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2
|
First
Semester
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100L
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11
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CHM
129
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PRACTICAL
CHEMISTRY
|
C
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1
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Second
Semester
|
100L
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12
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GSE
121
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AFRICAN
CULTURE, CIVILIZATION AND NIGERIAN PEOPLE
|
C
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2
|
Second
Semester
|
100L
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13
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PHY
129
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EXPERIMENTAL
PHYSICS11
|
C
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1
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Second
Semester
|
100L
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14
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PHY
121
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GENERAL
PHYSICS II
|
C
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3
|
Second
Semester
|
100L
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15
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CSC
121
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INTRO
TO OBJECT ORIENTED PROGRMMING
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C
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3
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Second
Semester
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100L
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16
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MTH
123
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VECTORS
AND DYNAMICS
|
C
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3
|
Second
Semester
|
100L
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17
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MTH
121
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GENERAL
MATHEMTICS11
|
C
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3
|
Second
Semester
|
100L
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18
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MTH
122
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THEORETICAL
STATISTICS
|
C
|
4
|
Second
Semester
|
100L
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19
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GSE
211
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PHILOSOPHY
AND LOGIC
|
C
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3
|
First
Semester
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200L
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20
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CSC
212
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INTRODUCTION
TO FILE PROCESSING
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C
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2
|
First
Semester
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200L
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21
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CSC
211
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COMPUTER
PROGRAMING1
|
C
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4
|
First
Semester
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200L
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22
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MTH
215
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STATISTICAL
METHODS
|
C
|
3
|
First
Semester
|
200L
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23
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MTH
214
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ESTIMATION
THEORY
|
C
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3
|
First
Semester
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200L
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24
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MTH
213
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LINEAR
ALGEBRA1
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C
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2
|
First
Semester
|
200L
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25
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MTH
212
|
SET,
LOGIC AND ALGEBRA
|
C
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3
|
First
Semester
|
200L
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26
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MTH
211
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MATHEMATICAL
METHODS1
|
C
|
3
|
First
Semester
|
200L
|
27
|
GSE
221
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COMUNICATION
IN ENGLISH11
|
C
|
2
|
Second
Semester
|
200L
|
28
|
CSC
222
|
INTRODUCTION
TO COMPUTES SYSTEMS
|
C
|
2
|
Second
Semester
|
200L
|
29
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CSC
221
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COMPUTER
PROGRAMING11
|
C
|
3
|
Second
Semester
|
200L
|
30
|
MTH
226
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INTRODUCTION.
TO OPERATION RESEARCH
|
R
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2
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Second
Semester
|
200L
|
31
|
MTH
225
|
REAL
ANALYSIS1
|
C
|
3
|
Second
Semester
|
200L
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32
|
MTH
224
|
PROBABILITY11
|
R
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4
|
Second
Semester
|
200L
|
33
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MTH
223
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NUMERICAL
ANALYSIS 1
|
C
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3
|
Second
Semester
|
200L
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34
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MTH
221
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ELEMENTARY
DIFFERENTIAL EQUATION
|
C
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3
|
Second
Semester
|
200L
|
35
|
MTH
222
|
LINEAR
ALGEBRA 11
|
C
|
2
|
Second
Semester
|
200L
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36
|
MTH
315
|
VECTOR
& TENSOR ANALYSIS
|
C
|
3
|
First
Semester
|
300L
|
37
|
GSE
311
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ENTREPRENEURIAL
SKILLS
|
C
|
2
|
First
Semester
|
300L
|
38
|
MTH
317
|
OPERATION
RESEARCH
|
E
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3
|
First
Semester
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300L
|
39
|
MTH
316
|
APPLIED
PROBABILITY
|
C
|
3
|
First
Semester
|
300L
|
40
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MTH
314
|
REAL
ANALYSIS II
|
C
|
3
|
First
Semester
|
300L
|
41
|
MTH
313
|
COMPLEX
ANALYSIS 1
|
C
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3
|
First
Semester
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300L
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42
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MTH
312
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DIFFERENTIAL
EQUATION
|
C
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3
|
First
Semester
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300L
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43
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MTH
311
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ABSTRACT
ALGEBRA 1
|
C
|
3
|
First
Semester
|
300L
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44
|
MTH
320
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INDUSTRIAL
TRAINING
|
C
|
6
|
Second
Semester
|
300L
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45
|
MTH
321
|
METRIC
SPACE TOPOLOGY
|
C
|
3
|
Second
Semester
|
300L
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46
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MTH
322
|
ABSTRACT
ALGEBRA II
|
C
|
3
|
Second
Semester
|
300L
|
47
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MTH
323
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INTRO.
TO MATHEMATICAL MODELING
|
C
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3
|
Second
Semester
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300L
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48
|
MTH
414
|
OPTIMIZATION
|
E
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3
|
First
Semester
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400L
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49
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MTH
413
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GENERAL
TOPOLOGY
|
C
|
3
|
First
Semester
|
400L
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50
|
MTH
412
|
FUNCTIONAL
ANALYSIS
|
C
|
3
|
First
Semester
|
400L
|
51
|
MTH
411
|
ORDINARY
DIFFERENTIAL EQUATION
|
C
|
3
|
First
Semester
|
400L
|
52
|
MTH
416
|
TIME
SERIES
|
E
|
3
|
First
Semester
|
400L
|
53
|
MTH
415
|
COMPLEX
ANALYSIS II
|
C
|
3
|
First
Semester
|
400L
|
54
|
MTH
422
|
LEBESQUE
MEASURE & INTEGRAL
|
C
|
3
|
Second
Semester
|
400L
|
55
|
MTH
423
|
NUMERICAL
ANALYSIS II
|
E
|
3
|
Second
Semester
|
400L
|
56
|
MTH
424
|
SYSTEM
THEORY
|
E
|
3
|
Second
Semester
|
400L
|
57
|
MTH
400
|
PROJECT
|
C
|
6
|
Second
Semester
|
400L
|
58
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MTH
421
|
PARTIAL
DIFFERENTIAL EQUATION
|
C
|
3
|
Second
Semester
|
400L
|
GSE 111 COMMUNICATION IN
ENGLISH
2 Credit Units
Effective
communication in English, Language skills in listening, speaking, reading and
writing. Aspects of sound patterns in English, units of grammar, types and
functions of clauses, composition, types, and functions of paragraph, Writing
style, Structuring the Essay, Essay, Dictionary; A study Aid, Word Choice and
Usage, The values of literature in the learning of the use of English.
Punctuation marks, Direct and indirect reported speech. Voice: active and
passive, tense, concord/agreement, Interpretation. Exercises in reading,
Comprehension, writing and listening. Phonetics, arts of public speaking and
oral communication, figures of speech. Research skills, writing of term of term
papers and research papers.
BIO 111 GENERAL BIOLOGY I 3
Credit Units
Cell
structure and organization; functions of cellular organelles; diversity,
Characteristics and Classification of living things, General reproduction,
interrelation of organisms; heredity and evolution
;
elements of ecology and types of habitat. Classification, similarities,
differences of the kingdom plantae. Adaptations of plants to their environment
highlighting the evolutionary trend. Biodiversity, Evolution, Genetics and
Hereditary. Current advances in plant biology, highlighting plant structure,
physiology, development and diversity. An analysis of geography of higher
plants, emphasizing process that operate at the species population level, the
origin and diversity of higher plant life, geographic patterns of diversity and
floras, and dynamics of species populations at local and continental scales.
BIO 119 PRACTICAL BIOLOGY I 1
Credit Unit
Practical
classes in plant cells and tissues. Internal and external features of plants.
Current methods used in plant research.
GSE 112 USE OF LIBRARY
1 Credit Unit
History
of library, library and education, university libraries and other types of
library and other types of library; study skills (reference services), types of
library materials, using library resources including e-learning, e-materials
etc. understanding library catalogues and classification; copyrights and its
implications, database resources, bibliographic citation and referencing.
CSC 111 Introduction to Computer
Science
3 Credit Units
History
of Computers, functional component of computer. Characters of a computer,
problem solving; flow charts, algorithms, computer programming. Statements and
symbolic names. Arrays, subscripts, expressions and control statements.
Introduction to Basic programming language, computer applications.
MTH
111 General Mathematics 1 3 Credits
Trigonometric Functions of angles of any
magnitude, addition and factor formulae, Complex numbers – Sum , Difference,
Product and quotient of complex numbers, polar form, Argand diagram, locus
problems, De Moivre’s theorem. Elementary set theory, subsets, union,
intersection and Venn diagram. Real numbers: integers, rational and irrational
numbers. Mathematical Induction, real
sequences and series. Theory of quadratic equations, Partial Fractions and
binomial theorem.
MTH
112 Data Analysis 2 Credits
Data Collection, presentation and EDA – Sample
surveys, experiments and observational studies. Scales of measurement.
Frequency distributions and diagrams including bar charts, histograms, and
scatter plots. Sample statistics (mean, median, mode, range, standard
deviation, coefficient of variation, quartiles, skewness, kurtosis, product
moment and rank correlation, Index numbers).
Estimation and Inference – Sampling distributions.
Distribution of sample means and proportions, variances. Confidence intervals.
Testing the value of single sample means, proportions and variances. Comparing
two means, proportions, variances. Chi-squared test of association and
Homogeneity.
GSE 121 AFRICANS CULTURES,
CIVILIZATION & NIGERIA PEOPLE 2 Credit Units
The
individual, society, environment, language, ethnicity, race and culture;
dynamics of culture change with reference to cultural and social history vis-Ã -vis
archeological studies; African cultural history and progress from the earliest
times, to the present with special mention of features such as farming,
metallurgy, trade union and rural life. Rural and urban life Nigeria with
emphasis on the socio-cultural and ecological factors predisposing to the rural-urban
dichotomy, family, economics, politics, and belief system.
GSE 211 PHILOSOPHY, LOGIC AND
CONFLICT RESOLUTION 2 Credit
Units
Introduction
to the nature of philosophy; its scope, problems and key concepts, The nature
and scope of logic. Laws of thought as aid to rational inquiry and their role
in the formation of arguments. The role of logical equivalence and conditional
statements. Kinds of logical equivalence and logical and their definition in
symbolic logic. The roles of inference and their application in the evaluation
of resolution. Peace and vehicle of unity and development. Conflict issues,
types of conflicts, causes of conflicts and violence in Africa, the
indigene/settler phenomenon, peace building, conflict management, peace
mediation and peace keeping, alternative dispute resolution, role of
international organization such as ECOWAS, African Union and United Nations in
peace keeping and conflicts resolution.
GSE 311 ENTREPRENEURIAL SKILLS
2 Credit Units
Introduction
to entrepreneurship and new ventures creation; Theory and practice of
entrepreneurship ; The opportunity, forms of business; staffing, Marketing and
the new venture; determining capital requirements, raising capital; financial
planning and managements. Starting a new business feasibility studies;
innovation; legal issues; insurances and environment considerations. Possible
business opportunities in Nigeria; case studies.
BIO 121 GENERAL BIOLOGY II
3 Credit Units
A
generalized survey of plant and animal kingdoms based mainly on the study of
similarities and differences in external features; ecological adaptations of
these forms. Classification, similarities and differences of the Kingdom
Animalia. Adaptive features of the various phyla. A study of diversity of
animals, their structure, physiology and evolution. Special emphasis is placed
on the unique features of fishes and their functional adaptations to aquatic
environments. A study of fish biology (icthyology), including anatomy,
systematic, physiology, behaviour, and ecology of fresh water and marine
fishes.
BIO 129 PRACTICAL BIOLOGY II 1 Credit
Unit
Practical
classes on features of animals from simple unicellular organisms to complex
mammals. Recent advances in animal study.
MTH 121
General Mathematics II 3 Credits
Function of a real variable and their graphs.
Treatment of limits and continuity. Derivatives as limits of rate of change.
Differentiation techniques, including products, quotients, etc. Extreme curve
sketching, Partial Derivative. Integration as an inverse of differentiation .
Methods of Integration. Integration techniques including substitution, parts
and partial fractions. Differentiation and Integration of Logarithm and
exponential functions, trigonometric and hyperbolic functions and their
inverses. Definite integrals. Applications to areas and volumes.
MTH 122
Theoretical Statistics 4 Credits
Probability Theory – Set Theory and Venn diagrams,
probability measures and axioms, mutually exclusive events, addition law,
conditional probabilities, multiplication law, conditional independence,
multiplication law, tree diagrams, Bayes Theorem, independence. Permutations
and Combinations.
Probability distributions and expectation –
discrete and continuous random variables. Probability (density) functions and
distribution functions. Expectation. Moments.
Sums and difference of random variables.
Probability Models – Bernoulli, Geometric,
Binomial, Poisson, Uniform, Exponent and Normal distributions. Test of hypothesis.
Test of hypothesis concerning the parameters of distributions. Test of
hypothesis concerning the patterns of distributions.
Modeling – Fitting and testing simple linear
models to data using regression techniques, Analysis of contingency tables.
MTH 123
Vectors and Dynamics 3 Credits
Geometric representation of Vectors in 1-3
dimensions, components, direction cosines. Addition and Scalar Multiplication
of Vectors. Scalar and Vector Products of two vectors. Differentiation and
integration of two vectors with respect to a scalar variable. Two-dimensional
co-ordinate geometry. Straight lines, circles, parabola, ellipse, hyperbola.
Tangents and normals. Kinematics of a particle. Components of Velocity and
acceleration of a particle moving in a plain. Force, momentum, laws of motion
under gravity. Projectiles, resisted vertical motion, elastic string, simple
pendulum impulse. Impact of two smooth spheres and of a sphere on a smooth
sphere.
MTH 211
Mathematical Methods I 3 Credits
Real-valued functions of a real variable. Review
of differentiation and integration and their application. Mean value theorem.
Taylor series. Real valued function of two or three variables. Partial
derivatives chain rule, extrema, language multipliers, Increments, differentials
and linear approximations. Evaluation of line, integrals.
MTH 212
Set, Logic and Algebra 3 Credits
Introduction to the language and concepts of
modern Mathematics. Topics include: Basic set theory, mappings, relations,
Cartesian Products. Binary logic, methods of proof. Binary operations.
Algebraic structures, semigroups, rings, integral domain fields. Homeomaphics.
Number systems;properties of integars, rationals, real and complex numbers.
MTH 213
Linear Algebra I 2
Credits
Vector space over the real field. Sub spaces,
linear independences, basis and dimension. Linear transformations and their
representation by matrices – range, null space, rank. Singular and non-sigular
transformations and matrices.
MTH 214
Estimation Theory 3
Credits
Estimation Theory – Properties of estimator,
unbiasness, efficiency, sufficiency, consistency and invariance. Method of
moments. Method of maximum likelihood. Method of least squares. Interval
estimation
Bayesian Decision Theory. Hypothesis Testing.
Types of error. Power analysis. Likelihood ratio tests-Neyman Pearson lemma,
Cramer-Roa Inequality, Best Asympotic Normality.
MTH 215
Statistical Methods 3 Credits
Distribution free procedures – Parametric vs. non-parametric
tests, power robustness. Sign, signed Rank, Sum of Rank tests. Chi-squared
test. Rank transformations.
Analysis of designed experiments – Completely
randomized design, Randomized Blocks. Factorial designs. Multiple Comparisons.
Analysis of residuals. Transformations. Model Fitting – Estimation and
inference relating to multiple linear regression models. Sampling methods –
Industrial sampling. Process control charts for means, proportions and range.
CSC 211 Computer Programming I 4
Credit Units
Introduction
to problem solving methods and algorithm development; designing, coding,
debugging and documenting programs using techniques of a good programing style.
Computer organization, Programming language and program algorithm development.
FOTRAN or any other widely used programming language will be used in teaching
the above.
CSC 212 Introduction to File
Processing 3 Credit Units
Introduction
to data management files; and job-control language application; an overview of
I/O (Input/output) system architecture; logical file organizations; mapping
logical organization unto physical storage; Back-up processing procedure, file
recovery, Higher level language data management data facilities.
MTH 221 Elementary Differential
Equation 3 Credit Units
First
order differential equations. Existence and uniqueness. Second order
differential equations with constant co-efficients. General theory of nth order
linear equations. Laplace transform, solution of initial-value problems by
laplace transform method. Single treatment of partial differential equations in
two independent variables. Application of O.D.E and P.D.E to physical life and
social sciences.
MTH 222 Linear Algebra II 2
Credit Units
Systems
of linear equation, change of basis, equivalence and similarity. Eigenvalues
and eigenvectors. Minimum and characteristic polynomials of linear
transformation (Matrix). Caley – Hamilton theorem. Bilinear and quadratic
forms, orthogonal diagnolisation. Canological forms.
MTH 223 Numerical Analysis I 3 Credit Units
Solution
of algebraic and transcendental equations. Curve fitting. Error analysis.
Interpolation and application. Zeros and non-linear equations to one variable. Systems
of linear equations. Numerical differentiation and integral equations. Initial
value problem for ordinary differential equations.
MTH 224 Probability II 4 Credit Units
Combinatorial
analysis. Probability model for the study of random phenomena in finite spaces.
Probability distribution of discrete and continuous random variables. Expectations
and moment generating functions. Cebyshev’s inequality. Bivariate, marginal and
conditional distribution and moments. Convolution of two distributions, the
central limit theorem and its uses.
MTH 225 Real Analysis
3 Credit Units
Bounds
of real numbers, convergence of sequence of numbers. Monolone sequences, the
theorem of nested intervals, Cauchy sequences, tests for convergence of series.
Absolute and conditional convergence of series, ad rearrangements. Completeness
of reals and incompleteness of rationals. Continuity and differentiability of
functions R…) R. Rolles and mean value theorems for differentiable functions.
Taylor series.
MTH 226 Introduction to Operations
Research 2
Credit Units
Formulation
and solution of LP problems: graphical and simplex method. Sensitivity analysis
and duality. Big M and phase1-phase11 methods. Transportation problems:
assignment and transhipment problems
CSC 221 Computer Programming
II 3 Credit Units
Principles
of good programming; structured programming concepts; Debugging and testing;
string processing, Internal searching and sorting, Data structures, recursion.
C++ or any other widely used programming language will be used in teaching the
above.
CSC 222 Introduction to Computer
Systems 2 Credit Units
Computer
Structure, machine language, assembly language, addressing techniques macros,
File I/O; Assembler segmentation and linkage; assembler construction;
interpretive routines.
MTH 311 Abstract Algebra I 3 Credit Units
Group theory: definition, subgroup, cosets. Lagrange’s theorem and applications. Cyclic groups, Rings, definitions and examples to include Z, Zn, Rings of polynomials and matrices, Integral domain, fields polynomial rings, factorization. Euclidean algorithm for polynomials H.C.F and L.C.M of polynomials.
MTH 312 Differential Equations 3 Credit Units
First order differential equations, Existence and uniqueness. Second order ordinary differential equations with constant coefficients. General theory of nth order linear equations. Laplace transformation, solution of initial value problems by Laplace transform method. Simple treatment of partial differential equations in two independent variables. Applications of O.D.E and P.D.E to physical, life and social sciences.
MTH 313 Complex Analysis I 3 Credit Units
Functions of complex variable, Limits and continuity of functions of complex variable. Derivation of Cauchy-Riemann equations. Analytic functions. 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 314 Real Analysis II 3 Credit Units
Riemann integral of functions, continuous monopositive functions, Functions of bounded variation. The Reimann-Stieltjes integral. Pointwise and uniform convergence of sequences and series. Effects of limits(sums) when the functions are continuously differentiable on Riemann integrable power series.
MTH 315 Vector and Tensor Analysis 3 Credit Units
Vector algebra, Vector dot and cross products. Equation of curves and surfaces. Vector differentiation and application. Gradient, divergence and curl. Vector integration, line surface and volume integral. Green stokes and divergence theorems. Tensor products of vector spaces. Tensor algebra and symmetry. Cartesians tensors.
MTH 316 Applied Probability 3 Credit Units
Probability Generating Functions (PGF) - Definition of pgf, pgf of sums of random variables. Branching processes - Galton-Watson model, probability of extinction. Random walks - Simple random walk, gambler’s ruin. Markov Chains - Stationary transition probabilities, transition matrix, classification of states, Chapman-Kolmogrov equations, n-step and limiting distributions. Stochastic Models - Examples from finance, management, biology and ecology. Poisson Process - Random events in time, exponential model, multi variance Poisson process, compound Poisson process. Birth Date Processes - Birth process, kolmogrov forward equations, Largrange’s equation, death process, simple birth and death process, embedded process.
MTH 317 Operation Research 3 Credit Units
Classification of operation research models. Integer and dynamic programming, Decision theory, two-person zero-sum games Inventory models, critical path analysis and project controls.
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