Mathematics — Study Path Agent

Chapter 1

Foundations: logic, proof, and sets

1

Mathematical language: statements, quantifiers, and definitions

2

Basic logic: connectives, truth tables, implication, contrapositive

3

Proof methods I: direct, contradiction, contrapositive

4

Proof methods II: induction, strong induction, invariants

Chapter 2

Numbers & algebra

5

Number systems: integers, rationals, reals, complex; absolute value

6

Algebraic manipulation: factoring, expansions, simplification, radicals

7

Equations & inequalities: linear, quadratic, systems; interval notation

8

Polynomials & rational expressions: roots, division, asymptotes

9

Exponentials & logarithms: laws, solving equations, change of base

Chapter 3

Functions & calculus

10

Functions: domain/range, composition, inverses; transformations

11

Limits & continuity: intuitive + formal limit laws; one-sided limits

12

Differentiation: rules, implicit diff, applications (optimization, related rates)

13

Integration: antiderivatives, substitution, area/accumulation; FTC conceptually

14

Infinite series (calculus): convergence tests; Taylor series basics

Chapter 4

Geometry & trigonometry

15

Euclidean geometry: angles, triangles, circles; similarity & congruence

Chapter 5

Linear algebra

16

Systems of linear equations: Gaussian elimination; solution sets

17

Vectors, span, linear independence; subspaces

18

Matrices & linear maps: multiplication, inverses, determinants (meaning first)

19

Eigenvalues/eigenvectors; diagonalization (conceptual + computation)

Chapter 6

Probability & statistics

20

Combinatorics: counting, permutations/combinations, binomial theorem basics

21

Probability basics: sample spaces, conditional probability, Bayes' rule

22

Random variables & distributions: expectation/variance; common distributions

23

Statistical inference: sampling, confidence intervals, hypothesis tests (intro)

Chapter 7

Discrete math & algorithms (intro)

24

Discrete structures: graphs, trees, relations, recursion (overview)

25

Modular arithmetic & number theory basics: gcd, Euclid algorithm, congruences

26

Algorithms & complexity (intro): big-O, searching/sorting ideas