Expert: Paul Klarreich - 12/29/2009

Question
after studying the following amount of math what further and in what order should I study  advanced math ?
Prealgebra
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Operations

Whole Numbers

Decimals

Fractions

Percents

Integers and Rationals

Powers, Exponents, and Roots

Measurements

Perimeter and Area

Variables

Review of Prealgebra
Geometry I
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Building Blocks of Geometry

Constructions

Polygons

Circles

Surfaces

Review of Geometry I
Geometry II
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Geometric Measurements

3-D Measurements

Special Triangles

Congruence

Geometric Theorems

Review of Geometry II
Geometry III
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Inductive and Deductive Reasoning

Logic Statements

Axioms and Postulates

Geometric Proofs

Review of Geometry III
Algebra I
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Expressions and Equations

Applications of Solving Equations

Inequalities

Compound Inequalities

Absolute Value

Probability

Graphing Data

Graphing Equations

Writing Equations

Systems of Equations

Variation

Exponents

Scientific Notation

Polynomials

Quadratics

Review of Algebra I
Algebra II
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Binomial Expansion

Factoring

Matrices

Rational Expressions

Complex Numbers

Functions

Operations on Functions

Discrete Functions

Inequalities

Operations with Functions

Special Graphs

Exponential Functions

Logarithmic Functions

Polynomials

Systems of Three Equations

Review of Algebra II
Trigonometry
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Angles

Graphs

Trigonometric Equations

Trigonometric Functions

Trigonometric Identities

Solving Oblique Triangles

Solving Right Triangles

More Trigonometric Identities

Review of Trigonometry
Precalculus
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Complex Numbers

Conic Sections

Continuity and Limits

Functions

Trigonometric Functions

Polynomial Functions

Parametric Equations and Polar Coordinates

Exponential and Logarithmic Functions

Sequences and Series

Review of Precalculus
Calculus AB
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Functions, Limits, and Continuity

Introduction to Derivatives

Applications of the Derivative (AB)

Introduction to Integrals

Inverse, Exponential, and Logarithmic Functions

Review of Calculus AB
Calculus BC I
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Introduction to Calculus BC

Functions, Limits, and Continuity

The Derivative

Computing Derivatives

Applications of the Derivative (BC)

Definite Integral

Review of Calculus BC I
Calculus BC II
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Computing Integrals

Applications of the Integral

Series

The Taylor Series

Parametric and Polar Curves

Review of Calculus BC II  

Answer
Wow!  Anyway, I suggest that you want to:

1. Complete Calculus -- partial derivatives, vectors, multiple integrals, differential equations.

2. Study analysis -- limits, continuity.(This time, you really mean it.)

3. Real variables and measure theory.

4. Complex variables

5. Probability.

6. Abstract algebra.

7. Number theory.

That should keep you busy for a few years.  Come back then and ask again.