MAT 100 - Precalculus

Syllabus for MAT 100 - Precalculus

This is a compulsory course for BS Mathematics students in their 1^st semester.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: None

Overview: Introduction to modern mathematical language and reasoning: Sets and Functions, Proofs, Number Systems, Limits.

Detailed Syllabus:

1. Sets: Describing sets – roster and set-builder notation, empty set, subsets and equality, power set, finite and infinite sets, the language of logic (and, or, not, quantifiers), union, intersection, complement, Euler and Venn diagrams, algebra of sets, Cartesian product

2. Relations and Functions: Relations, functions, real functions and their graphs, increasing & decreasing functions, transformations of functions and their graphs, algebra of functions, composition, one-one functions, onto functions, inverse of a function

3. Number Systems: Review of N, Z and Q, mathematical induction, sup and inf, order completeness of R, Archimedean property of R, applications of completeness (existence of square roots, real powers), C.

4. Catalog of Real Functions: Polynomial functions and graphs, division of polynomials, factor theorem, rational functions, exponential functions, logarithmic functions, trigonometric functions, trigonometric graphs

5. Limits: Estimating limits numerically, examples of existence and non-existence, limit laws, applications of limit laws, one-sided limits, tangent lines and derivatives, limits at infinity, limits of sequences

References:

1. Precalculus by James Stewart, Lothar Redlin and Saleem Watson. Cengage. 5^th ed.
2. Understanding Mathematics by K B Sinha et al, Universities Press.