### Mathematics for Science 2020 BCS, BIT, BSE & BCT

Purpose:

To provide students with basic mathematical tools and abilities of algebra, trigonometry, permutation and combinations, series and complex numbers

Teaching methodology:  Lectures, tutorials; and group discussions

Course Assessment:

Continuous Assessment                      30%

End of Semester Examination            70%

 LECTURE/WEEK COURSE CONTENT REMARKS 1 Surds, logarithms and indices; 2 Determination of linear laws from experimental data; Quadratic functions, equations and inequalities 3 Remainder theorem and its application to solution of factorisable polynomial equations and inequalities; 4 Permutations and combinations; 5 Cat 1/ Assignment 1 6 Series: finite, infinite, arithmetic, geometric and 7 Binomial series, and their applications such as compound interest, approximations, growth and decay; 8 The principle of induction and examples such as formulae for summation of series and properties of divisibility; 9 Trigonometry; trigonometric functions, their graphs and inverses for degree and radian measure, addition, multiple angle and factor formulae, trigonometric identities and equations; 10 Cat 2 /Assignment 11 Sine and cosine formulae; their application to solution of triangles, trigonometric identities; 12 Complex numbers: Argand diagrams, arithmetic operations and their geometric representation; Modulus and argument; 13 De Moivre’s theorem and its applications to trigonometric identities and roots of complex numbers.

Course Textbooks

1. Uppal S.M. and Humphreys H.M. (2008). Mathematics for Science, (2nd Ed.). New Delhi, India: New Age International Pvt Ltd Publishers. ISBN-13: 978-8122409949
2. Backhouse J.K. (2007). Pure Mathematics 1 (4th Ed.). NY, USA: Longman. ISBN-13: 978-0582353879
3. Sullivan M. (2011). Algebra and Trigonometry (9th Ed.). Canada: Pearson Education. ISBN-13: 978-0321716569

Reference Textbooks

1. McKeague C.M. (2011). Elementary Algebra, (9th Ed.). New Delhi, India: Cengage Learning. ISBN-13: 978-0840064219
2. McKeague C.M. (2009). Basic Mathematics, (7th Ed.). New Delhi, India: Cengage Learning. ISBN-13:978-0534378929
3. Aufmann R.N., Barker V.C. and Nation R.D. (2007). College Algebra and Trigonometry (6th Ed.). Boston, USA: Houghton Mifflin. ISBN-13: 978-0618825158 MAT 2111 MATHEMATICS FOR SCIENCE OUTLINE Dr.docx

### Discrete Structures (BSE/BCS Groups)

Course Description

Propositional logic: propositions, logic operators and truth tables, tautologies and contradictions, logical equivalence, boolean algebra, normal forms.

Methods of proof: direct proof, proof by contrapositive, proving equivalence, predicates  and quantifiers, mathematical induction, proof by contradiction.

Integers: binary, Hexadecimal and Base-n representation, modulo operations, divisibility, GCD and LCD, the Euclidean algorithm, sequences, recurrence relations, finding primes.

Sets and counting: set operations, venn diagrams, set identities, power sets, cross product, cardinality, the  pigeon hole principle, the  inclusion-exclusion  principle, permutations and combinations.

Binary relations: properties of relations, digraphs, equivalence relations and equivalence classes, partial order, Hasse diagrams, total order, zero-one matrices, transitive closure.

### organization management

this course will enable the learner to understand an organization and how it is set up and managed.

The course will involve group research, discussion, and presentation of real companies registered in Kenya and demonstration of the organization setup