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Math
124 topics across 7 chapters
Chapter 1
Foundations
1
Arithmetic & Number Sense
3 subtopics
2
Integers & Order of Operations (PEMDAS)
3
Fractions, Decimals, and Percents
4
Ratios, Rates, and Proportions
5
Sets & Logic Basics
3 subtopics
6
Set Notation & Operations (Union, Intersection, Complement)
7
Propositional Logic & Truth Tables
8
Quantifiers and Predicate Logic (∀, ∃)
9
Mathematical Reasoning & Proof
3 subtopics
10
Direct Proof and Contrapositive
11
Proof by Mathematical Induction
12
Proof by Contradiction & Counterexamples
13
Functions Basics
3 subtopics
14
Domain, Range, and Function Notation
15
Graph Transformations & Function Composition
16
Inverse Functions & One-to-One Tests
Chapter 2
Algebra
↗ Functions Basics (see Chapter 1)
17
Expressions & Equations
3 subtopics
18
Linear Equations and Inequalities
19
Quadratic Equations (Factoring, Completing the Square, Formula)
20
Rational Equations & Extraneous Solutions
21
Polynomials
3 subtopics
22
Factoring Techniques (GCF, Trinomials, Special Products)
23
Polynomial Division & Remainder Theorem
24
Zeros, Multiplicity, and End Behavior
25
Exponents & Logarithms
3 subtopics
26
Exponent Rules and Radical Exponents
27
Logarithm Rules & Change of Base
28
Solving Exponential and Logarithmic Equations
29
Systems of Equations
3 subtopics
30
Solving Linear Systems (Elimination, Substitution)
31
Matrix Methods for Systems (Augmented Matrices)
32
Nonlinear Systems (Intro) and Intersections
Chapter 3
Geometry & Trigonometry
33
Euclidean Geometry
3 subtopics
34
Triangle Congruence & Similarity
35
Circle Geometry (Chords, Tangents, Inscribed Angles)
36
Area and Volume Formulas (2D/3D)
37
Coordinate Geometry
3 subtopics
38
Distance, Midpoint, and Slope
39
Lines (Point-Slope, Slope-Intercept) and Intersections
40
Conics (Intro): Parabolas, Ellipses, Hyperbolas
41
Trigonometric Functions
3 subtopics
42
Unit Circle, Radians, and Reference Angles
43
Core Trig Identities (Pythagorean, Sum/Difference)
44
Solving Trig Equations & Graphing Trig Functions
45
Vectors in 2D/3D
3 subtopics
46
Vector Addition and Scalar Multiplication
47
Dot Product, Angles, and Projections
48
Cross Product and Area/Volume Applications
Chapter 4
Calculus
↗ Functions Basics (see Chapter 1)
49
Limits & Continuity
3 subtopics
50
Limit Laws and One-Sided Limits
51
Computing Limits (Factoring, Conjugates, Basic Trig Limits)
52
Continuity and the Intermediate Value Theorem
53
Differentiation
3 subtopics
54
Derivative Definition & Basic Rules
55
Chain Rule & Implicit Differentiation
56
Applications of Derivatives (Optimization, Related Rates)
57
Integration
3 subtopics
58
Antiderivatives and the Fundamental Theorem of Calculus
59
u-Substitution and Basic Integration Techniques
60
Applications of Integrals (Area, Volume, Accumulation)
61
Series & Approximations
3 subtopics
62
Sequences and Convergence (Basics)
63
Taylor Polynomials and Local Approximation
64
Power Series and Convergence Tests (Overview)
65
Multivariable Calculus (Intro)
3 subtopics
66
Partial Derivatives and Tangent Planes
67
Double Integrals (Intro) and Regions in the Plane
68
Gradients and Lagrange Multipliers (Intro)
Chapter 5
Discrete Mathematics
↗ Sets & Logic Basics (see Chapter 1)
↗ Mathematical Reasoning & Proof (see Chapter 1)
69
Combinatorics
3 subtopics
70
Counting Principles (Sum/Product Rules)
71
Permutations and Combinations
72
Binomial Theorem & Inclusion–Exclusion (Intro)
73
Graph Theory
3 subtopics
74
Graph Terminology and Representations (Adjacency, Matrices)
75
Trees and Spanning Trees
76
Shortest Paths (BFS/Dijkstra Concepts)
77
Number Theory Basics
3 subtopics
78
Divisibility, Prime Numbers, and Factorization
79
Modular Arithmetic and Congruences
80
Greatest Common Divisor & Euclidean Algorithm
Chapter 6
Probability & Statistics
81
Probability Foundations
3 subtopics
82
Sample Spaces, Events, and Axioms
83
Conditional Probability and Bayes’ Theorem
84
Independence and Basic Probability Calculations
85
Random Variables & Distributions
3 subtopics
86
Discrete Random Variables (PMF, Expectation, Variance)
87
Continuous Random Variables (PDF/CDF)
88
Common Distributions (Binomial, Normal, Poisson)
89
Statistical Inference
3 subtopics
90
Confidence Intervals (Means/Proportions Basics)
91
Hypothesis Testing (z/t Tests Basics)
92
p-Values, Type I/II Errors, and Power (Basics)
93
Regression & Modeling
3 subtopics
94
Simple Linear Regression (Least Squares Intuition)
95
Multiple Regression (Basics) and Interpretation
96
Model Diagnostics and Overfitting (Intro)
97
Data Analysis Practice
3 subtopics
98
Descriptive Statistics & Data Visualization
99
Sampling, Bias, and Experimental Design (Basics)
100
Compute/Simulate Statistics with Software (Excel/R/Python)
Chapter 7
Linear Algebra
↗ Vectors in 2D/3D (see Chapter 3)
101
Vector Spaces & Subspaces
3 subtopics
102
Span, Linear Independence, and Basis
103
Subspaces and Dimension
104
Orthogonality and Gram–Schmidt (Intro)
105
Matrices & Linear Systems
3 subtopics
106
Matrix Multiplication and Inverses
107
Row Reduction and RREF
108
Solve Ax=b and Interpret Solutions Geometrically
109
Determinants & Eigenvalues
3 subtopics
110
Determinants: Meaning, Properties, and Computation
111
Eigenvalues and Eigenvectors
112
Diagonalization and Applications (Intro)
113
Linear Transformations
3 subtopics
114
Linear Transformations as Matrices
115
Change of Basis (Intro) and Coordinate Systems
116
Applications: 2D Transforms and Markov Chains (Intro)

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