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About
TMUA Handouts
TMUA Handouts
A1 Algebra Basics
A2 Equations and Inequalities
A3 Exponents and Logarithms
B Mathematical Logic Basics
C Sequences and Series
D Coordinate Geometry
E Trigonometry
F Differentiation
G Integration
H Logic and Counterexamples
I Functions and Graphs
J Sets and Probability
K Number Theory and Combinatorics
L Proof Methods
M Comprehensive Training
N Mock Exam Sprint
History of Math
Lecture 1: The Pythagorean Theorem
Lecture 2: The Foundations of Greek Geometry
Lecture 3: Greek Number Theory and Arithmetic
Lecture 4: The Concept of Infinity in Greek Mathematics
Lecture 5: The Wisdom of Number Theory in the East—China and India
Lecture 6: The Algebraic Breakthrough—Solving the Cubic and Quartic
Lecture 7: The Birth of Analytic Geometry—The Marriage of Algebra and Geometry
Lecture 8: Surface Curvature and the Catenoid
Teaching Notes
Teaching Notes
s2
S2 Chapter 1: The Binomial Distribution
S2 Chapter 2: The Poisson Distribution
S2 Chapter 3: Approximations and the Central Limit Theorem
S2 Chapter 4: Continuous Random Variables
S2 Chapter 5: The Uniform Distribution
S2 Chapter 6: Sampling Distributions
S2 Chapter 7: Hypothesis Testing
Further Math
FP2 Chapter 1: Inequalities
FP2 Chapter 2: Series — Method of Differences
FP2 Chapter 3: Complex Numbers and de Moivre's Theorem
FP2 Chapter 4: Further Argand Diagrams
FP2 Chapter 5: First-Order Differential Equations
FP2 Chapter 6: Second-Order Differential Equations
FP2 Chapter 7: Maclaurin and Taylor Series
FP2 Chapter 8: Polar Coordinates
FP3 Chapter 1: Hyperbolic Functions
FP3 Chapter 2: Further Coordinate Systems
FP3 Chapter 3: Differentiation
FP3 Chapter 4: Integration
FP3 Chapter 5: Vectors
FP3 Chapter 6: Further Matrix Algebra
M2 Lecture Notes: A Historical Journey through Mechanics
M2 Mechanics: Kinematics of Motion in Two Dimensions
M2 Mechanics: Statics — Centres of Mass and Equilibrium
M2 Mechanics: Work, Energy, Impulses and Collisions
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Teaching Notes
Teaching Notes
Section titled “Teaching Notes”
Pedagogical materials, lecture handouts, and teaching reflections.
S2 Statistics
Section titled “S2 Statistics”
Chapter 1: The Binomial Distribution