MATH1025: Preparatory mathematics
Preparatory mathematics notes.
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Course contents
MATH1025: Preparatory mathematics
Preparatory mathematics notes.
Chapter 0-1
Foundations and early methods
Foundational symbolic language and core transformations used across the course.
0.1 Course foundations and notation
Set up notation, proof habits, and algebraic prerequisites that support later trigonometry, sequences, and vectors.
1.1 Equation structure and trigonometric identities
Reinforce equation-solving structure and trigonometric identities with proof-aware algebraic transformations.
Chapter 2-3
Proof and inequalities
Induction, order reasoning, rational inequalities, absolute value, and first classical inequalities.
Chapter 4
Binomial theorem
Factorials, permutations, combinations, Pascal's identity, and coefficient extraction from binomial expansions.
4.1 Binomial coefficients and expansions
Connect permutations, combinations, Pascal's identity, and the binomial theorem.
Chapter 5
Sequences
Sequences as functions, recursive construction, arithmetic and geometric progressions, finite sums, and first applied recurrences.
5.1 Sequences, recursion, and series
Read sequences as functions on positive integers, compare explicit and recursive definitions, and derive arithmetic and geometric sum formulas.
Chapter 6
Complex numbers
Complex arithmetic, conjugates, modulus, polar and exponential forms, roots of unity, and complex-plane geometry.
6.1 Complex numbers, polar form, and geometry
Construct complex numbers from ordered pairs, use conjugates and polar form, and connect rotation, roots of unity, and complex-plane geometry.