Math Major First Year

ALGEBRA I (MATH1034/5) (65 lectures)

The first 2/5ths of this topic equips the students with a collection of standard mathematical concepts, these being:

Radian measure
Proofs of the trigonometric identities
The Cartesian-plane - the concept of distance, the triangle inequality, circles in the plane
Lines in the plane - parametric and implicit representations
Inequalities
The absolute value function
The concept of a function, domains and ranges of functions, the graph of a function, odd and even functions, one-to-one and onto functions, inverses of functions, composite functions
Inverse trigonometric functions
Polar coordinates and sketching curves specified in polar coordinates
Mathematical induction
Sigma notation and telescoping series
The factorial function and the Binomial theorem
Conic Sections
Vectors in R2

The remaining 3/5ths of the topic are based on the first 3 chapters of the textbook "Elementary Linear Algebra" by Anton and Rorres. The material covered includes:
Addition, subtraction and scalar multiplication of matrices
Products of matrices and its interpretation
The transpose operation
Matrix powers and polynomials
Invertible matrices
Elementary matrices
Construction of inverses
Solution of AX=B for a general matrix A
Determinants and their properties
The adjoint and Cramer s rule
Rank of a matrix
Vectors in R3
Complex numbers
CALCULUS I (MATH1036/7) (91 lectures)

This is based on the textbook "Thomas Calculus, Early Transcendentals (11th ed)" by Weir et al, Pearson.

Limits and Continuity
Differentiation
Applications of Differentiation
Hyperbolic functions
Partial Derivatives
Integration
Transcendental functions
Applications of integration
Integration techniques
Sequences and series
Differential Equations