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Beginnercounting, shapes, first sums

1Counting and shapes
2Numbers to 100
3Adding and subtracting to 20
4Place value to 1,000

Easymultiplication, fractions, decimals, ratios

5Multiplication and first fractions
6Long division and equivalent fractions
7Fraction and decimal arithmetic
8Ratios and negative numbers
9Proportional reasoning

Intermediatealgebra, geometry, functions

10Pre-algebra
11Algebra 1
12Geometry
13Algebra 2
14Trigonometry and precalculus

Advancedcalculus, statistics, university maths

15Calculus 1
16Calculus 2
17Statistics and probability
18Multivariable calculus
19Linear algebra
20Differential equations
21Proofs and discrete maths
22Probability theory

Expertmaths major and graduate topics

23Real analysis
24Abstract algebra
25Complex analysis
26Topology
27Electives
28Measure theory
29Functional analysis
30Graduate algebra
31Algebraic topology
32Smooth manifolds
33Qualifying exams
34Choose a field
35Advanced courses and reading
36Advisor and thesis problem
37Original research and dissertation

Step 21: Proofs and discrete maths

Proofs and discrete maths: final exam