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SEMESTER TWO & SEMESTER ONE COURSE DETAILS
KAMPALA UNIVERSITY
DEPARTMENT OF NATURAL SCIENCES
MATHEMATICS
DEGREE COURSE OUTLINES
ALL COURSES ARE COMPULSORY IN FIRST YEAR FOR MAJOR AND MINOR
YEAR ONE LH TH CH CU
SEMESTER 1
BMTC: 1101 Element of Mathematics 30 15 45 3 BMTC:1102 Linear Algebra I 30 15 45 3 BMTC:1103 Differential Calculus 30 15 45 3 BMTC:1104 Integral Calculus 30 15 45 3 SEMESTER 2 BMTC;1201 Vector Calculus 30 15 45 3 BMTC:1202 Elements of Probability & Statistics
BMTC:1203 Classical Mechanics 30 15 45 3 BMTC:1204 Mathematics Education I 30 15 45 3 YEAR TWO SEMESTER 1 CORES : BMTC:2101 Mathematics Analysis I 30 15 45 3 BMTC:2102 Complex Variables 30 15 45 3
ELECTIVES
BMTC: 2111 Differential Equations 1 30 15 45 3 BMTC: 2112 Number Theory 30 15 45 3 BMTC: 2113 Discrete Mathematics 30 15 45 3 SEMESTER 2 CORES: BMTC:2201 Mathematics Education II 30 15 45 3 BMTC:2202 Numerical Analysis I 30 15 45 3 ELECTIVES BMTC: 2211 Probability Theory 30 15 45 3 BMTC: 2212 Computer Science 30 15 45 3 BMTC: 2213 Graph Theory 30 15 45 3 YEAR THREE SEMESTER 1 BMTC: 3101 Mathematics Analysis II 30 15 45 3 BMTC: 3102 Abstract Algebra 30 15 45 3 ELECTIVE: BMTC: 3111 Linear Programming 30 15 45 3 BMTC: 3112 Inferential Statistics 30 15 45 3 SEMESTER 2 CORES: BMTC:3201 Operations Research [Project in Mathematics]
Credit Units: 3CU Brief Course Description : This is the course that emphasizes learning and understanding mathematical techniques, together with their applications to specific problems. It is an extension of Differential Calculus and Integral Calculus. Some of the topics covered include: Vectors in the plane and space, Motion and vector valued functions, Partial differentiation, Multiple integrals and Vector analysis
Course Objectives:
By the end of this course students should be able to:
i. Sketch and analyze curves given parametrically-graph curves in polar coordinates
ii. Compute areas and arc lengths using rectangular and polar coordinates
iii. Recognize and apply algebraic and geometric properties of vectors in two and three
dimension
iv. Compute dot product and cross products and recognize their geometric meaning
v. Visualize and sketch surfaces in three dimensional space
vi. Compute and interpret partial derivatives of several variables and apply them in finding
maxima and minima values of functions in two variables
vii. Evaluate double and triple integrals using a variety of coordinate systems, including
rectangular, polar, cylindrical and spherical
viii. Apply double and triple integral in finding area & volume of different surfaces
Expected Learning Outcome:
On successful completion of this course unit, students should be:
Able to show an understanding of concepts, principles, procedures and applications of
Calculus.
Able to express themselves in proper mathematical language and formulate problems in
the mathematics language.
Apply their knowledge of calculus to find solutions to real–life problems that involve
changing situations.
Detailed Course Content Topic Sub-Topic Hours
- Vectors •: Vector and Scalar quantities •: Definition and denotation of a vector •:Magnitude, equality, opposite and resultant of vectors •:Algebra of vectors; Addition, subtraction, multiplication, division.
- Laws of vector algebra
- Unit vectors. rectangular unit vectors and Parallel vectors
2 Scalar and vector products
- Dot product and its applications
- Cross product and its applications
- Triple product, vector identities and other applications 05 3.Vector equation of line and plane
- Vector equation of line
- Intersection of lines
- Distance of a point from a line
- Equation of a plane
- Shortest distance from a point to a plane
- Angle between two planes
- Intersection of two planes
4 Vector functions • Vector valued functions
- Triple integrals Total credit hours 45 Methods of Delivery: Lecture, discussions and group work Methods of Assessment: Assessment Marks % Coursework (At least two tests/ assignments) 30 End of Semester Examination 70 Final Mark 100 Recommended References
Core text books
1. Dalton Tarwater (2008); Analytical Geometry. N.Y.; Addison Wesley
2. Jervold Marson (2008); Vector Calculus ;N.J; W. H Free man and Company
3. Rawat,K.S. (2008); Vector Analysis. New Delhi; Sarup And Sons (publishers)
4. Spiegel M ((1984); Vector Analysis Schaum Series outline; London; McGraw -Hill
Recommended Text Books
- Heard T. (1986), Mechanics and vectors , N.J: Cambridge University Press
2. Holder Leonard (1984); Primer for Calculus (3rd Edition. N.J ; Wadworth
3. Marson J E (2006); Vector Calculus. London; V H Free man & Co. Ltd.
4. Larson R. and Edwards H. B., (2013). Calculus 10th Edition. Stamford, Connecticut:.
Cengage Learning
Course Name: ELEMENTS OF PROBABILITY AND STATISTICS Contact Hours:45hours Course Code: BMTC: Course Level: Year One Semester: Two Credit Units: 3CU Brief Course Description : This course provides a short introduction to the basic elements of probability and statistics, methods of data handling and some standard statistical tests/inferences. The main aim of this course is to provide the students the basic knowledge and ideas of how to handle statistical work, analyze any statistical
data and interpret the findings. Students are guided on how to use statistical tools to summarize the information for easy interpretation. Areas to be covered include: Descriptive Statistics, Elementary Probability theory, Counting theory, Descriptive Statistics, Random Variables, Probability Distributions, Estimation and Simple Regression Analysis.
Objectives of the Course
By the end of the course, students will be able to:
i. Calculate values of descriptive statistics
ii. Compute probabilities of given problems
iii. Obtain estimates of unknown parameters
Expected Learning Outcome:
Upon completion of this course the students should be able to apply basic Statistical Methods to analyze a given data set and to fit a simple linear regression model to the data for further analysis Detailed Course Content Topic Sub-Topic Hours
- Statistics • Introduction
- Definition and key concepts
- The importance of statistics in general
- Data
- Data Collection
- Data organizing
- Processing
- Analysis,
- Interpretation and presentation
- Dissemination (publication) of processed data
mean and variance of continuous random variable, Binomial distribution, Chebyshev’s Theorem
7.Common distributions Geometric distribution, Hyper geometric distribution, Poisson distribution, Rectangular distribution, Exponential distribution, Normal distribution, Student’s t – distribution, Chi-square distribution, F– distribution and their applications to real life experiences
8.Estimation and Sampling theory Introduction
- Point estimation
- Interval estimation
- Confidence intervals
- Population and samples
- sample and Population means
- Sampling designs and procedures e.g. simple random sampling, cluster sampling, systematic sampling etc.
Total credit hours 45 Methods of Delivery: Lecture, discussions and group work Methods of Assessment: Assessment Marks % Coursework (At least two tests/ assignments) 30 End of Semester Examination 70 Final Mark 100 Recommended References Core text books 1.Biswal, P.C. (2009); Probability And Statistics. New Delhi ; Prentice-hall Of India Pvt Ltd
2.Casella G. & Berger R. L. (2002). Statistical inference , 2nd Ed, N.Y; Duxbury/ Thomson Learning,.
- Mann.P. (2005); Introduction to Statistics. N.Y; John Wiley and Sons
- Silvey S. O. (2008); Statistical Inferences ; C. London.; Brown Publishers
- Spiegel,M.R.,Schiller,J.& Srinivasan,R.A. (2009). Probability and Statistics, 3rd edition. New York; McGraw Hill. Recommended Text Books 1.Lyman R. O & Longnecker M, (2001) An Introduction to Statistical Methods and Data Analysis 5th Edition , 5511 Forest Lodge Road, Pacific Grove, CA 93950 USA, Wadsworth Group. (Classic book)
- Ruma Falk (2003); Understanding Probability and Statistics : A Book Of Problems. London ; Oxford Universities Press 3.Walpole R.E. (1982), Introduction to Statistics , New York; Macmillan. (Classic book)
- Suhov,Y.& Kelbert.M. (2005); Probability and Statistics by Example: Basic Probability and Statistics( Volume 1 ). New York ; Cambridge University Press Course Name: CLASSICAL MECHANICS 1 Contact Hours:45hours Course Code: BMTC: Course Level: Year One Semester: Two Credit Units: 3CU Brief Course Description : The study of mechanics is to help the students understand the behavior of inert matter and the objects of which matter is the building material. For objects which move with speeds much less than that of light and which have dimensions large compared with those of atoms and molecules Newtonian mechanics, also known as classical mechanics, is nevertheless quite satisfactory. For this reason it has maintained its fundamental importance in science and engineering. Single particle and many particles situations are considered.
Objectives of the Course
- Forces in equilibrium, , , , ,
- Moments and couples
- friction,
- General conditions for equilibrium
- Rigid body systems
- Systems of coplanar forces
- Light framework
- Jointed rods/beams.
- Motion-Newton’s laws of motion, work , energy and momentum
- Newton’s laws
- Definitions of force and mass
- Units of force and mass
- Work, power, kinetic energy
- Conservative force fields
- Potential energy and conservation of energy
- Impulse, torque and angular momentum
- Conservation of momentum
- Non-conservative forces
- Statics or equilibrium of a particle
- Hookes law and simple harmonic motion
- Work, power, energy and conservation of energy
- Simple harmonic motion and damped harmonic oscillator
4 Motion Motion in a uniform field,
falling bodies and projectiles
- Uniformly accelerated motion
- Weight and acceleration due to gravity
- Gravitational system of units
- Assumption of a flat earth
- Freely falling bodies
- Projectiles
- Potential and potential energy in a uniform field
- Motion in a resisting medium
- Isolating the system
- Constrained motion
- Friction
- Statics in a uniform gravitational field
- The simple harmonic oscillator and the simple pendulum
- The simple harmonic oscillator
- Amplitude, period and frequency of simple harmonic motion
- Energy of a simple harmonic oscillator
- The damped harmonic oscillator
- Over damped, critically dumped and under damped motion
- Forced vibrations
- Resonance
- The simple pendulum
Total credit hours 45 Methods of Delivery: Lecture, discussions and group work
iii Design school teaching syllabi of mathematics at both O-level and A-level iv. Construct suitable items for an effective assessment. v. Design a school teaching syllabi of mathematics at both o-level and A-level
Expected Learning Outcome:
On successful completion of this course unit, students should be:
Apply their knowledge of Mathematics Education to find solutions to real–life problems that
involve changing situations.
Detailed Course Content Topic Sub-Topic Hours
- Mathematics teaching and learning. •: Why teach mathematics •: Goals and aims why we teach mathematics •:Nature of mathematics •:Mathematics needs of adult life
2 Syllabi and schemes of work
- The school teaching syllabus
- Scheme of work
- Lesson plan 05
- Theories of learning:, • Theory of piaget and implications to T/L
- Theory of Bruner and implications to T/L
- Theory of Skemp and implications to T/L
- Theory of Diennes Zoltan and implications to T/L
- Theory of Gagne and implications to T/L
4 Mathematics teaching styles
- Exposition by the teacher
- Small and large group discussions
- Problem solving stages by George Polya an Burton 06
- Mathematical investigations
- Continuity of Vector valued functions
- Differentiability of Vector valued functions
- Integration of Vector valued functions
- Shortest distance from a point to a plane 5 Fundamentals affecting teaching attainment in mathematics
- Attitudes and individual differences
- Gender differences,
- Teaching in second language and problems of technical language
- Teaching environment
- Cognitive and social cognitive constructivist theories •: Constructivist theory by Piaget, Bruner and Skemp •: Implication of cognitive constructivist theory to T/L of mathematics •: Social cognitive constructivist theory by Levi Vygotsky
- Implication of Levi Vygotsky’s social cognitive constructivist theory to T/L of mathematics
- Test construction and construction of marking guides
- Bloom’s taxonomy ie recall, comprehension, application and synthesis
- Specification table use in test construction.
- Marking and marking guide construction 06
- Affective domain and mathematics achievement
- Self-concept and students’ mathematics achievement
- Emotional intelligence and students’ mathematics achievement 06
Course Level: Year Two Semester: Two Credit Units: 3CU Brief Course Description : This course provides undergraduate students with both theoretical and practical background knowledge and understanding of the field of mathematics education.
Course Objectives:
By the end of this course students should be able to:
i Engage self exposition skills that should enable them to teach mathematics competently ii. Prepare both the scheme of work and lesson plans regularly iii Design school teaching syllabi of mathematics at both O-level and A-level iv. Construct suitable items for an effective assessment.
Expected Learning Outcome:
On successful completion of this course unit, students should be:
Apply their knowledge of Mathematics Education to find solutions to real–life problems that
involve changing situations.
Detailed Course Content Topic Sub-Topic Hours 1.Mathematics curriculum at secondary school •: Definition of curriculum •: Types of curriculum •:Factors that could bring about mathematics curriculum change
- Criteria for selection of mathematics curriculum content
- Barriers to mathematics curriculum development
- Curriculum designs
2 Philosophies of teaching • Idealism
mathematics and curriculum perspectives
- Realism
- Existentialism
- Pragmatism
- Positivism
- Naturalism
- Testing, assessment, evaluation and appraisal
- Definition and types of tests
- Rowntree’s five dimensions of assessment
- Evaluation vs assessment
- Formative and summative assessment
- Purposes of evaluation and assessment
- Various assessment models and purpose of preparing marking guides
4 Technology use in T/L mathematics
- Selection, preparation, use and management of mathematics teaching resources in schools
- Use of realia
- Use of calculators
- Calculators and computers in a mathematics classroom, their operations and uses
5 Professional development of teachers of mathematics
- Career patterns of mathematics teachers
- The supply of mathematics teachers and there deployment and duties of a head of department
- Professional development of teachers of mathematics
Total credit hours 45 Methods of Delivery: Lecture, discussions and group work
