Study Path Agent Study Path Agent
Generate Your Own
Math
164 topics across 7 chapters
Chapter 1
Mathematical Foundations
1
Numbers & Operations
4 subtopics
2
Integers, Fractions, Decimals
3
Ratios, Percent, Proportions
4
Exponents & Roots
5
Order of Operations & Estimation
6
Notation, Logic & Sets
4 subtopics
7
Propositional Logic Basics
8
Set Operations & Venn Diagrams
9
Quantifiers & Negation
10
Mathematical Definitions & Counterexamples
11
Problem-Solving Strategies
4 subtopics
12
Units & Dimensional Analysis
13
Pattern Recognition
14
Translating Word Problems
15
Checking Solutions & Reasonableness
Chapter 2
Algebra
16
Expressions & Equations
4 subtopics
17
Simplifying Expressions
18
Solving Linear Equations
19
Solving Quadratic Equations
20
Rearranging Formulas
21
Polynomials & Factoring
4 subtopics
22
Polynomial Arithmetic
23
Factoring Techniques
24
Rational Expressions
25
Completing the Square
26
Inequalities
3 subtopics
27
Interval Notation
28
Linear Inequalities
29
Quadratic & Rational Inequalities
30
Systems of Equations
3 subtopics
31
Substitution & Elimination
32
Systems with Matrices (2x2, 3x3)
33
Word Problems with Systems
34
Exponentials & Logarithms
4 subtopics
35
Laws of Exponents
36
Logarithm Properties
37
Solving Exponential/Log Equations
38
Growth & Decay Models
39
Functions
4 subtopics
40
Function Notation & Evaluation
41
Domain & Range
42
Graph Transformations
43
Inverse Functions & Composition
Chapter 3
Geometry & Trigonometry
44
Euclidean Geometry
4 subtopics
45
Angles, Triangles, Congruence
46
Similarity
47
Circles
48
Area & Volume
49
Coordinate Geometry
3 subtopics
50
Distance & Midpoint
51
Lines & Slopes
52
Conic Sections Basics
53
Trigonometry
4 subtopics
54
Radians & Unit Circle
55
Right-Triangle Trig
56
Trig Identities
57
Solving Triangles & Applications
58
Geometric Proofs
3 subtopics
59
Proof with Congruence
60
Proof with Similarity
61
Coordinate Proof
62
Vectors
3 subtopics
63
Vector Addition & Scalar Multiplication
64
Dot Product
65
Vector Projections
Chapter 4
Calculus
↗ Functions (see Chapter 2)
66
Limits & Continuity
3 subtopics
67
Limit Laws
68
One-sided & Infinite Limits
69
Continuity & Intermediate Value Theorem
70
Derivatives
5 subtopics
71
Definition of Derivative
72
Differentiation Rules
73
Implicit & Logarithmic Differentiation
74
Applications: Optimization
75
Related Rates
76
Integrals
4 subtopics
77
Antiderivatives
78
Definite Integrals & Fundamental Theorem of Calculus
79
Integration Techniques (u-sub, parts)
80
Applications: Area & Volume
81
Sequences & Series
4 subtopics
82
Arithmetic & Geometric Sequences
83
Series Tests (ratio, comparison)
84
Power Series
85
Taylor/Maclaurin Series
86
Multivariable Calculus Basics
4 subtopics
87
Partial Derivatives
88
Multiple Integrals
89
Gradient & Directional Derivatives
90
Optimization with Constraints (Lagrange multipliers)
Chapter 5
Discrete Mathematics
91
Proof Techniques
3 subtopics
92
Direct & Contrapositive Proof
93
Proof by Contradiction
94
Mathematical Induction
95
Combinatorics
3 subtopics
96
Permutations & Combinations
97
Binomial Theorem
98
Inclusion–Exclusion Principle
99
Graph Theory
3 subtopics
100
Graph Terminology (paths, cycles, degree)
101
Trees & Spanning Trees
102
Shortest Paths & Connectivity
103
Number Theory
3 subtopics
104
Divisibility & Modular Arithmetic
105
Euclidean Algorithm (gcd)
106
Primes & Factorization
107
Recurrence & Discrete Complexity Basics
3 subtopics
108
Recurrence Relations
109
Big-O Notation Basics
110
Solving Linear Recurrences (characteristic roots)
Chapter 6
Probability & Statistics
111
Probability Fundamentals
3 subtopics
112
Sample Spaces & Events
113
Conditional Probability & Bayes’ Rule
↗ Permutations & Combinations (see Chapter 5)
114
Random Variables & Distributions
4 subtopics
115
Discrete Random Variables (binomial, geometric)
116
Continuous Random Variables (normal, exponential)
117
Expectation & Variance
118
Law of Large Numbers & Central Limit Theorem (basics)
119
Descriptive Statistics
3 subtopics
120
Measures of Center & Spread
121
Data Visualization (histograms, boxplots)
122
Correlation
123
Inferential Statistics
3 subtopics
124
Sampling & Confidence Intervals
125
Hypothesis Testing & p-values
126
Common Tests (t, chi-square)
127
Regression & Data Analysis
3 subtopics
128
Linear Regression
129
Residuals & Model Diagnostics
130
Overfitting & Validation Basics
Chapter 7
Applied & Advanced Topics
131
Linear Algebra
4 subtopics
132
Vectors, Matrices, Systems
133
Determinants
134
Eigenvalues & Eigenvectors
135
Linear Transformations
136
Differential Equations
4 subtopics
137
First-order ODEs
138
Second-order Linear ODEs
139
Systems of ODEs
140
Qualitative Phase Portraits (basics)
141
Optimization & Numerical Methods
3 subtopics
142
Numerical Root Finding (bisection, Newton)
143
Numerical Integration
144
Gradient Descent Basics
145
Complex Numbers
3 subtopics
146
Complex Plane & Arithmetic
147
Euler’s Formula
148
Roots of Unity
149
Mathematical Modeling
3 subtopics
150
Dimensional Modeling
151
Building & Validating Models
152
Modeling with Differential Equations (concepts)
↗ Proof Techniques (see Chapter 5)
153
Intro to Real Analysis
3 subtopics
154
Sequences & Limits (epsilon idea)
155
Continuity & Differentiability (analysis view)
156
Convergence of Series (analysis view)

Want a personalized study path for any topic?

Generate Your Own Study Path