This publication provides the needed basic information on academic programs, rules and regulations of the department of Mathematics, Ebonyi State College of Education, Ikwo. 

The department of Mathematics, within the School of Sciences was established in the year 2000 at the inception of the college. Since then, it has been growing and waxing very strong along side with other departments in the college academic programs. However it is worth mentioning that there is presently low student enrolment in all academic programs in colleges of education nation wide including mathematics department.

Development of Mathematics is unique, because Mathematics as a discipline is the chief servant, queen and bride of other disciplines, the bedrock and data processing center of the sciences. This write up will form an available reference material on academic expectations for the students in the department or those who would want to enroll into the department most especially the year one students.

Staff, students and others who may have one thing or the other to do with the department will find information in this publication very useful. This write up will clear the conflicts, misunderstanding, misinformation and other cases that may arise about the department from time to time.

Continuing and incoming students will no doubt find the information in this publication very useful throughout their stay in this college.

Philosophy of NCE Mathematics Education

The philosophy of NCE Mathematics is inspired by the desire to help 

1. students become intellectually informed in Mathematics ideas, notations and skills for logical reasoning, scientific enquiry and for the pursuit of techno-scientific education
2.  produce non-graduates but well-groomed and qualified professional teachers of mathematics for the Basic Education Levels.

Objectives of NCE Mathematics Education

By the end of the program, students who were certified worthy in learning by the requirement of the program should be able to:

1. Discuss with confidence the historical development of mathematics as a discipline.
2. Solve abstract problems through the use of mathematic skills and ideas.
3. Stimulate pupils interests in mathematics by the use of appropriate teaching/learning strategies particularly at the Basic education levels.
4. Make learners appreciate the use of computers in solving mathematical problems.
5. Use mathematics to solve day to day problems.
6. Teach mathematics in a way that learners can apply mathematics principles in solving daily problems.
7.  Make the teaching of mathematics learner friendly through games and 
8. Set up a mathematics laboratory.
9. Prepare the learners for further studies in mathematics and related courses.

General Admission Requirements

1. Senior Secondary School Certificate of WAEC or NECO or any other equivalent Certificate from recognized examination bodies with credit passes in  four (4) subjects including English Language and Mathematics at not more than two sittings. Two of the credits must be in the subjects making up the combinations the candidates wish to offer. 
2. A Grade II Teacher's Certificate (TC 11) with credit or merit in four (4) subjects, two of which must be relevant to the course the candidate wishes to offer. 
3. It should be noted that the college may in addition to all the above, administer her own elimination tests and/or interviews for some courses. This is legitimate.

Summary of Admission Requirements into NCE Mathematics

Candidates seeking for admission to NCE Mathematics should obtain a credit pass in at least four subjects including Mathematics and English language at SSCE (WAEC or NECO) or GCE 'O' Level or merit or a credit pass in TC II.

Subject Combinations

The following subject combinations with Mathematics within School of Science exist:

1. Mathematics / Biology, 
2. Mathematics / Physics 
3. Mathematics / Computer Science, 
4. Mathematics / Chemistry 
5. Mathematics/Integrated Science 
6. Mathematics / Geography

However, other combinations with Mathematics involving course from other schools exist as approved by National Commission of Colleges of Education.

Graduation Requirements

Each student is required to carry a minimum of 118 credits and a maximum of 122 credits before graduation. The breakdown is as follows:  

Mathematics                      -         Minimum      32          Maximum     34       Credits

Second Teaching Subject   -         Minimum      32          Maximum     34       Credits

Education Including TP      -         Minimum      36          Maximum     36       Credits

General Studies                  -         Minimum      18          Maximum     18       Credits

          Total                      -         Minimum     118          Maximum    122     Credits

Teaching Practice

Teaching Practice is compulsory for every student before   graduation Teaching Practice earns 6 credits under (EDU 311).

Project

The Final Year Project is compulsory for all students. The Project may be written and supervised in any of the student's chosen subject areas and the grade for Project must be credited to EDU 323. Project carries 2 credits.

Evaluation and assessment Methods

1. Continuous Assessment (C.A)     40% 
2. End of Semester Examination      60%

Attendance

A registered student for the N.C.E. Program must attain a 75% attendance to be allowed to write the end of the Semester Examination.

Assessment and certificate mode

(i)      Continuous Assessment (CA) =40%

(ii)     Examination = 60%

COURSE CONTENTS AND OBJECTIVES

NCE I   FIRST SEMESTER

Course Codes, Titles Credit Units and Status

MAT 111:    ALGEBRA                       

2 Credits      Compulsory

Objectives

By the end of course students should be able to discuss and solve simple problems in algebra.

Course Content

• Real number system
• Integers, rational and irrational numbers
• Set theory, intersection, complement of set, venn diagram, Algebra of sets.
• Theory of indices
• Theory of logarithms
• Surds
• Linear inequalities
• Partial fractions
• Theory of quadratic equations
• Permultations and Combinations
• Binomial
• Mathematical Induction
• Remainder and Factor Theorems
• Arithmetic progression
• Geometric Progression

MAT 112       TRIGONOMETRY

2 Credits        Compulsory

Objectives

At the end of course the student should be able to:

1. discuss with confidence the basic concepts and definition in trigonometry,
2. Solve simple problems using the concepts.

Course Content

• Angle and its measurements
• Basic trigonometric functions and equations
• Trigonometric ratios in each of the 4 quadrants. Applications to bearing, angle of elevation, depression and projectile
• Graphs of trigonometric functions and their applications 
• Inverse trigonometric functions
• Half angle formulae
• Addition of factor formulae
• Solution of triangles
• Hyperbolic functions and their identities

MAT 113       HISTORY OF MATHEMATICS                         

1 Credit        Compulsory

Objectives

At the end of course the student should be able to:

1. Discuss and narrate the historical development of mathematics as a discipline, 
2. Identity the early contributors to the development of mathematics.

 Course Content

• Pre-history Mathematics
• Development of Mathematics in the Ancient times
• Contributions of Babylonians, Greeks, Egyptians, Romans, Hindus, Arabs and Chinese.
•  Prominent Ancient Mathematicians and their contributions (Archimedes, Pythagoras, Euclid, Apollonius, etc.)
•  Development of mathematics in the Middle Ages and prominent Mathematicians of the period
• The Renaissance and Mathematics (16^lh to 20^th Centuries) and prominent mathematicians and their contributions (Napier, Fermat, Euler, Riemann, Lebesque, Lagrnge, Hilbert, Bannach, Catichy)
•  The use of mathematics in everyday life including its place in Natural and Applied science
• History of African and Nigerian mathematics

MAT 114     COMPLEX NUMBERS                                             

1 Credit        Compulsory

Objectives

At the end of course the student should be able to: 

1.  Explain the concepts of complex numbers
2. Discuss the algebra of complex numbers 
3. Represent complex numbers in argand diagrams
4. State De-moire theorem.
5.  Solve problems on complex numbers.
6.  Approve the important of complex number in science and technology.

            Course Content

• complex Numbers
• Algebra of Complex numbers
• Argand Diagram
• De Movie's theorem
• N^th root of Unity

MAT 115     STATISTICS

2 Credit        Compuslory 

Objectives

At the end of course the student should be able to:

1. Define the meaning of statistics
2. Discuss the importance of statistics 
3. Formation of frequency distribution table iv Calculation of measure of location, partition and dispersion 
4. Explain the meaning of correlation and regression 
5. Define sample space and sample point 
6. State and draw normal distribution curve and skewness
7. Carry out test of hypothesis and significance on sample data.

 Course Content

• Frequency distribution
• Measures of location
• Measures of dispersion
•  Correlation and Regression
• Sample Space and Sample point
• Data Representations in statistics
• Normal Distribution Curves
• Skewness
• Standardized Normal Curve
• t-scores and Z-scores
• Test of Hypothesis and significance

NCE I SECOND SEMESTER

MAT 121     DIFFERENTIAL CALCULUS

Objectives

By  the end of course the student should be able to: 

1. Differentiate some given function 
2. Apply differentiation in solving physical problems.

           Course Content

• Functions
• Limit of a function at a point
• Continuity of a function at a point
• Gradient of a function
• The differential co-efficient as a gradient of a function at a point
• Differential product and quotient
• The chain rule and the function of a function
• Differentiations of logarithmic functions
• Trigonometric functions, exponential functions and hyperbolic functions
• Implicit differentiation
• Applications: maximal, minimal, velocity, acceleration and rate of change

MAT 122     CO-ORDINATE GEOMETRY                                 

2 Credits      Compulsory

Objectives

By the end of course the student should be able to:

1. Obtain the equation of straight line and circle
2. write the equation of parabola, ellipse and hyperbola in Cartesian polar and parameter coordinator.
3. Change Cartesian coordinates to polar & vice versa
4. Apply the knowledge of coordinate geometry in solving real life problems.

           Course Content

• Basic Geometry :point' line segment, angle, curve
• Straight lines and circles
• Parabola, Ellipse and Hyperbola in Cartesian, parametric and polar co-ordinates
• Tangents and Normal to the circle, parabola, eclipse and hyperbola (the use of differentiation is acceptable

MAT 123     MATHEMATICS METHODOLOGY                       

2 Credits      Compulsory

Objectives

By  the end of course the student should be able to:

1.  Learn the most current method of teaching mathematics
2.  Write lesson plan & lesson notes in mathematics.

           Course  Content

• History of Mathematics teaching in Nigeria and the philosophy of current Nigerian Mathematics curricula
• Teaching and learning mathematics, including works of Bruner, Gagne, Piaget and Dienes
• Teaching of concepts, principles, skills and proofs: strategies, nature, definitions and types.
• Inductive, deductive, analytic and synthetic approaches in Mathematics teaching 
• Content analysis of upper basic education (JSS 1-3) curriculum
• Work tools( scheme of work,  Lesson plan, lesson presentation and Assessment)
• Hem construction and development of marking scheme
• Diagnosis and remediation of difficulty concepts and topics in teaching and learning of upper basic Mathematics curriculum
• Problems and prospects of mathematics education in Nigeria

MAT 124     MATHS LABORATORY PRACTICAL                       

1 Credit        Compulsory

Objectives

By the end of course the student should be able to:

1.  Construct, design and improvise some basic mathematical teaching aids. 
2. Construct triangle, quadrilaterals loci etc. using pair of compass and rulers.

            Course Content

• Construction, design and improvisation of some basic mathematical teaching aids in relation to primary, junior secondary school and senior secondary school courses. (Using cardboard sheets, clay wood, wires, etc)
• Geometrical constructions: construction of triangles, quadrilaterals, bisection of lines, angles and construction of locus.

MAT 125      INTRODUCTIONS TO COMPUTER STUDIES                 

1 Credit       Elective

Objectives

By the end of course the student should be able to:

1. State fundamental operations in mathematics structures and their uses in computer studies 
2. Define with example binary logic, compound statement and binary operations. 
3. Discuss historical development of the computer studies 
4. Differentiate between software and hard ware 
5. Write simple programme using basic. 
6. Apply the application to data processing plus operating systems e.g. Dos, windows

Course Content

• Historical development of the Computer
• Essential components of the Computer and their functions
•  Number presentation in a Computer
•  Logic:- Binary logic, compound statement-logic relations, methods of proofs, binary operations.
• Number bases other than 10
• Data structure and their uses in a Computer
• Computer software and types of software, Basic Programming
• Illustration and the application of simple techniques to Data processing plus-
• Operating systems: Dos, Windows etc.(Emphasis on practical)

NCE II         FIRST SEMESTER

MAT 211     INTEGRAL CALCULUS                       

2 Credits      Compulsory

Objectives

By the end of course the student should be able to:

a)  See the link between differentiation and integration.

b)  See the link between integration and area

c)  Identify and use of different integration methods.

d)  Use the different methods of integration in real engineering problems.

e)  Appreciate the importance of integration in engineering and science generally.

     Course Content

• Integration as a reverse process of differentiation
• Integration as area under the curve
• Integration of algebraic functions using different methods, like partial fractions, substitution, etc.
• Integration of non-algebraic functions e.g. logarithmic functions, exponential functions, trigonometric functions, etc.
• Special methods of integrations; substitution and transformation, the reduction formula and other types of systematic integration.
•  Integration by parts. Approximate integration by Trapezoidal rule and Simpson's Rule
• Application of integration in determining volumes of solids of revolution and solution to other problems

MAT 212     PROBLEM-SOLVING (JSS & SSS)                     

1 Credit        Compulsory

Objectives

(Textbooks on these levels should be provided at least two students to a copy of each) 

By  the end of course the student should be able to:

1. Identify what is a problem, and decide on the most appropriate approach to the solving problem.
2. Identify as many methods as possible to the solving of identified problems eg discovery, expository child centre approach etc.
3. See that life itself is problem, and always have solutions if given the right approach. Appreciate the different techniques so identified in solving day to day problems.

     Course Content

• Definitions of problem, problem solving
• Basic elements of a mathematics problem
• Common errors in Mathematics
• Discovery and expository approaches to problem solving techniques
• Functions of questions in the Mathematics class
• Characteristics of a good problem solver
• Polya's problem solving heuristics and application to solving topics in J.S.S. and
• S.S.S. Mathematics
• Problem solving of selected difficult topics in Mathematics and further
• Mathematics e.g. solid figures, great cycles, application of the cosine rule to triangles (acute and obtuse angle) e.t.c.

MAT 213     NUMBER THEORY                                             

1 Credit        Compulsory

At the end of course the student should be able to:

1. Be able to exhibit the proper concept of number system by correctly showing the direction and magnitude of numbers.
2. Be able to play and manipulate different ideas as to the use of numbers, eg : ordering of numbers, mathematical inductions, basic facts on numbers(theorem), congruence etc.
3. Be able to see and appreciate the use of numbers in the real life situations.

           Course Content

• Process of counting, Piano's Axons using ordered pairs
• Fundamental operations in Mathematical Structures 
• Group —Group properties
• Further properties of Integers
• Well ordering principle
• Mathematical Induction to Laws of tracheotomy
• Divisibility (Basic definitions, divisions, primes god) 
•  Basic theorems on god
• (proofs may be required)
• Relatively prime integers (unique factorization)
• The fundamental theorem of arithmetic (proof may be required)
• Congruences
• Basic definitions and examples
• Properties of Congruence (reflexive symmetric' and transitive: the equivalence relation)
• Residue classes
• Linear Congruences
• Basic theorems and solutions of linear Congruences
• Proofs of the main theorem may be required
• Format's theorem and applications, the proof of Format's theorem may be required
• Eiuler function and number (proof not required)
• Application to linear Congruences
• Fundamental operation in mathematical structures\
• Group properties.

MAT 214      PROBABILITY THEORY                                         

2 Credits      Compulsory

At the end of course the student should be able to:

1. Learn the concepts of probability
2.  Solve problems involving addition law, multiplication law of probabilities. Formulate hypotheses and arrive at the right decision.
3. Apply the knowledge of probability in other relevant situation 

          Course Content

• Concept of probability 
• Sampling and sampling techniques 
• Types of probability 
• The concept of expectation
• Mutually exclusive and non-mutually exclusive events 
• Addition law of probability 
• Independent events and dependent events
• Multiplication law of probability 
• Conditional probability 
• Discrete probabilities 
• Continuous probabilities 
• Functions of a random variable
• The Binomial Poisson and normal distribution with various properties; 
• Permutations and combination.

NCE II SECOND SEMESTER

MAT 221     DYNAMICS

1 Credits      Compulsory

At the end of course the student should be able to:

1. Explain the concept of displacement, speed, velocity and acceleration in Cartesian and polar co-ordinate.
2. Discuss relative velocity motion of particles in straight lines. State the principle of conservation of energy. State and discuss types of collision
3. Discuss the concept of projectiles, momentum vertical motion under gravity. 
4. Solve problems on dynamics.

          Course Content

• Displacement, Speed, Velocity and acceleration in Cartesian and Polar co-ordinates 
• Velocity and acceleration along the tangent and normal to it 
• Relative velocity, motion of particles in straight lines 
• Vertical motion under gravity (laws of motion)
• Projectiles: Time of (light, range on a horizontal plane, greatest height reached, the part of a projectile as parabola.
• The momentum equation and derivation of the impulse
• Angular momentum principles
• Impact of two small spheres (direct and oblique)
• The principle of conservation of energy.

MAT 222     VECTOR ANALYSIS                                   

2 Credits      Compulsory

Objectives

By the end of course the student should be able:

1. Represent vectors in 2-3 dimensions
2. Solve problems in vector algebra
3. Apply the knowledge of vector analysis in solving real life problems.

            Course Content

• Representation of vectors in 1-3 Dimensions
• Equality of vectors, position vectors (explain using the model of space co-ordinate)
• Triangular, parallelogram and polygon laws of vector addition 
• Resultant of vectors
• Associative law of vectors
• Negative and unit vectors
• Magnitude or length of a vector
• Commutative and distribution laws of vectors, Scalar or dot product of vectors
• The vector or cross product of two vectors
• The cosine of angles between two vectors
• Direction cosines
• Relations between dot product and component of work done in a force field
• Triple product of vectors
•  Plane and space curves and their vector equations
• Vector differentiation
• The grad notation
• The del (or vector operator notation)
• The divergence of a curve vector and the divergence theorem
• Frener —Serret formulae for solution of problems

MAT 223     REAL ANALYSIS I                                         

1 Credit        Compulsory

Objectives

By the end of course the student should be able to:

1. Solve abstract problems through the use of mathematical skills.
2. Use correctly the methods of proofs in mathematics.

   Course Content

• Basic properties of real number system including boundedness and completeness
• Concept of neighbourhood
• Open and close sets
• Basic theorems on open and closed sets
• De Morgan laws
• Function and functional notation
• Rigorous treatment of limits and continuity
• L'Hospital's rule (proof may be required)
• Consequences of differentiation
• Rolle's theorem
• Mean value theorem and Taylor's theorem (proof may be required)
• Successive differentiation
• Leibnitz's formula for nth derivative (proof not required)
• Functions of several variables
• Partial differentiation
• Lagrange's multipliers

MAT 224     JUNIOR SECONDARY SCHOOL CONTENT         

1 Credit        compulsory

Objectives

By the end of the course the students should be able to:

1. Learn by heart the sequential arrangements of all the topics in junior secondary school mathematics. 
2. Solve difficult problems in junior secondary school mathematics.

     Course Content

• Fractions decimals and approximation:-harder word problems involving fractions decimals and approximations.
• Expansion & factorization
• Simultaneous linear equations:-elimination, substitutions, graphical methods word problems leading to simultaneous equations.
• Quadratic equation by factorization only, word problems involving quadratic equations.
• Algebraic fractions & Algebraic equations, word problems involving algebraic equations 
• Pythagoras theorem and its applications
• Angles of elevation and depression
•  Properties of plane shapes:- cubes, cuboid, cylinder, spheres, pyramid and cones
• Areas and perimeters of plane shapes:- problems involving areas and perimeters, surface areas and volumes of solid shapes
• Variations :- Direct inverse, joint and partial variation including word problems
•  Trigonometric ratios and their application
• Commercial Arithmetic (profit and loss, discount hire purchase, commission), number basis.
• Scale drawing
• Areas and volumes of similar shapes.

MAT 225     RESEARCH METHODOLOGY         

1 Credit        compulsory

 Objectives

(Note: This course should be taken by students wishing to write their project in Mathematics Education)

Aim: the teaching of this course is aimed at preparing students to learn how to carry out research works in Mathematics Education without much difficulty.

         Course Content

1.  Research Study

a)  Background of the study

b)  Statement of problem

c)  Purpose of the study

d)  Scope of the study

e)  Area of the study

f)   Significance of the study

2.   Literature Review

The relevance of the review to the background of study must be clearly shown to the students.

3.   Method of data organization

a)  Techniques of getting the sample from sample population such as 

i)       Simple ballot system

ii)      Use of table of random numbers and any other iii) Slating the population and the sample

b)   Instrument for data collection

c)  Validation of instrument

d)  Analysis of data— Frequency table, percentages, t-test and x-test statistics,

e)  Correlation coefficient

f)  Results and Interpretation

g)  Recommendation

NCE III        FIRST SEMESTER

EDU 324

TEACHING PRACTICE

NCE III - SECOND SEMESTER

MAT 321     STATICS                         

1 Credits      Compulsory

Objectives

By the end of course the student should be able to: 

1. Explain with confidence the concept of statics. 
2. Solve simple problems on statics 
3. Justify the relevant of statics 
4. Resolution of forces and turning points practically 
5. Apply the concepts in solving problems.

           Course Content

• General conditions of equilibrium
• Resolution forces acting at a point
• Equilibrium conditions of moments
• Coplanar forces (centroids)
• Centre of gravity: centre of mass, simple forms, general formula for centre of gravity
• Compound bodies, centre of gravity by integration
• Friction: laws of friction and resistance, angle of friction, the least force problem involving sliding only

MAT 322      LINEAR ALGEBRA                                       

1 Credit        Compulsory

Objectives

By the end of course the student should be able to:

1. Discuss with confidence the concept and the meaning of linear algebra such as vector space over the real field, sub-space, linear independence, basis and dimension, linear transfunctions, eigenvalues etc.
2. solve simple problem on the linear algebra.
3. apply the knowledge of the concept to other areas.

            Course Content

• Matrices: definition, equality of matrices, addition, scalar multiplication, multiplication of matrices, inverse matrices, adjoint transpose, row equivalence and elementary row operations.
• Determinats:- up to 2x2 matrices.  Application of matrices to solutions of linear equations.
• Determinants
• Vector space over the real field, sub-space, linear independence, basis and dimension
• Linear transformations and their representational matrices; range, null space, rank, singular and non-singular transformation and matrices.
• System of-linear equations, change of basis, equivalence and similarities
• Higen values (latent roots) and given vectors (latent vectors)
• Minimum and characteristic polynomials of a linear transformation (matrix)
• Cayley - Hamilton theorem

MAT 323     REAL ANALYSIS II                                                       

2 Credits       Elective

Objectives

By the end of course the student should be able to:

1. Discus the meaning of anti-derivatives, reimann integral and its properties
2. Define and solve problem on multiple integrations, series and sequence.
3. Approve the relevant of real analysis in everyday life and for further studies 
4. Solve problems on real analysis

            Course Content

• Anti-derivative (Integration)
• Definition of Riemann integral
• Properties of Integrals and basic theorems (proof of the fundamental theorems of calculus may be required)
• Multiple Integration; elementary treatment of the Fubinis theorem in the plane
• Series and sequences
• Proof of boundedness; comparison, ratio and root test may be required
• Absolute and conditional convergence
• Radius of convergence
• Power series
• Uniform convergence

MAT 324     ABSTRACT ALGEBRA                                             

1 Credit        Elective

ALGEBRAIC STRUCTURES

Objectives

By the end of course the student should be able to: 

1. Explain the meaning of algebraic structure         
2. Define the following : group , semi group , monoid, group and subgroup
3.  State lag range theorem
4. Explain the concepts of cyclic group, ring, integral domain, field
5. Solve problems on polynomials: HCF,LCM and factorization

            Course Content

• Grouped, semi group, monoid and group, subgroup
•  Lagrange theorem, cyclic group, ring, integral domain, division, ring and field
• Polynomials: H.C.Fand L.C.M of polynomials
• Factorization

MAT 325     DIFFERENTIAL EQUATIONS                                 

1 Credit        Compulsory

Objectives

By the end of the course students should be able to:

1. Discuss the meaning of first-order differential equations
2. State the existence and uniqueness of solution.
3. Apply different methods of solving differential equations
4. Slate and solve second order differential equation
5. Approve the importance of differential equations in science and technology
6. Formation of differential equation using physical and chemical situations.

            Course Content

• First -order differential equations
• Existence and Uniqueness of solution
• Example to be limited to equations of the types 

• Use of boundary separation restricted only to easy integral 
•  Homogeneous Equations.
• Exact equations and integrating factor for non-exact equations
• Solution of 2^nd order differential equation.  Example to be restricted to the equations of the type.

 dx²                        dx² 

Equations with constant co-efficient and Cauchy-Euler types should be treated. Formation of equations from physical situations.

SUMMARY OF COURSE TITLES AND STATUS

Course codes, Titles, Credit Units and Status.

NOTE: Students are advised to take at least (2) two elective courses. 

          Compulsory must be passed and at least two elective courses.

          C = Compulsory 

          E = Elective Courses.