Mathematics Syllabus

Mathematics — 30-day syllabus

Stage I — Numbers & Algebra (Days 1–8)

Day	Topics	90-Day Sources
1	Integers, fractions & decimals	Days 1–3
2	Factors, primes & integer division	Days 4–5
3	Number bases & binary arithmetic	Days 6–7
4	Exponents, logarithms & Gate I	Days 8–10
5	Variables, linear equations & inequalities	Days 11–13
6	Systems, polynomials & factoring	Days 14–16
7	Rational expressions, functions & quadratics	Days 17–19
8	Exponential functions, summation & Gate II	Days 20–22

Stage II — Logic & Structures (Days 9–15)

Day	Topics	90-Day Sources
9	Propositional logic, Boolean algebra & normal forms	Days 23–25
10	Quantifiers & direct proof	Days 26–28
11	Contrapositive, cases & induction	Days 29–31
12	Strong induction, fallacies & Gate III	Days 32–34
13	Sets, set operations & Cartesian products	Days 35–37
14	Relations, equivalence relations & partial orders	Days 38–40
15	Bijections, composition, countability & Gate IV	Days 41–43, 46

Stage III — Counting & Graphs (Days 16–22)

Day	Topics	90-Day Sources
16	Types analogy & pigeonhole principle	Days 44–45
17	Counting rules, permutations & combinations	Days 47–49
18	Binomial theorem, stars-and-bars & inclusion-exclusion	Days 50–52
19	CS counting & recurrence relations	Days 53–55
20	Story proofs, counting workshop & Gate V	Days 56–58
21	Graphs, paths & trees	Days 59–61
22	BFS/DFS, DAGs & shortest paths	Days 62–64

Stage IV — Applied & Capstone (Days 23–30)

Day	Topics	90-Day Sources
23	Bipartite, Euler/Hamilton & graph coloring	Days 65–67
24	Graph modeling & Gate VI	Days 68–70
25	Divisibility, Euclidean algorithm & modular arithmetic	Days 71–73
26	Modular inverses, Fermat/Euler & hashing	Days 74–76
27	Crypto math, CRT, PRNGs & Gate VII	Days 77–80
28	Asymptotic notation & complexity analysis	Days 81–84
29	Probability, conditional probability & expectation	Days 85–87
30	Capstone dossier & retrospective	Days 88–90