Aaron Toponce

A photo of me and my library of math books that I studied to walk with a Bachelor's of Science in Applied Mathematics.

As of April 22, 2011, I have a Bachelors of Science degree in Mathematics, with an emphasis in applied math, and a minor in Computer Science, with an emphasis towards software development. While going through my college career in math, I wanted to take as many diverse electives as I could, while still maintaining the requirements for graduation in a timely manner. What resulted was not only study a great deal of applied mathematics, but also reaching the requirements for a an emphasis in general mathematics theory as well (even though the university won't give me a second emphasis).

Here are the classes I studied, and the topics discussed in each class:

Precalculus:

1. Graphs
2. Functions and Their Graphs
3. Polynomial and Rational Functions
4. Exponential and Logarithmic Functions
5. Trigonometric Functions
6. Analytic Trigonometry
7. Applications of Trigonometric Functions
8. Polar Coordinates and Vectors
9. Analytic Geometry
10. Systems of Equations and Inequalities
11. Sequences, Mathematical Induction and the Binomial Theorem
12. Counting and Probability

Single Variable Calculus I:

1. Function and Models
2. Limits and Rates of Change
3. Derivatives
4. Applications of Differentiation
5. Integrals
6. Applications of Integration

Single Variable Calculus II:

1. Inverse Functions
2. Techniques of Integration
3. Further Applications of Integration
4. Differential Equations
5. Parametric Equations and Polar Coordinates
6. Infinite Sequences and Series

Multivariate Calculus:

1. Vectors and the Geometry of Space
2. Vector Functions
3. Partial Derivatives
4. Multiple Integrals
5. Vector Calculus
6. Second-Order Differential Equations

Discrete Mathematics:

1. Logic, Sets and Functions
2. Algorithms, Integers and Matrices
3. Mathematical Reasoning
4. Counting
5. Advanced Counting Techniques
6. Relations
7. Graphs
8. Trees
9. Boolean Algebra
10. Modeling Computation

Ordinary Differential Equations:

1. Classifications
2. First Order
3. Second Order
4. Higher Order
5. Series Solutions of Second Order
6. The Laplace Transform

Elementary Linear Algebra:

1. Vectors
2. Solving Linear Equations
3. Vector Spaces and Subspaces
4. Orthogonality
5. Determinants
6. Eigenvalues and Eigenvectors
7. Linear Transformations
8. Applications of Linear Algebra

Probability and Statistics I:

1. Historical Summary
2. Probability
3. Random Variables
4. Special Distributions
5. Estimation

Dynamical Systems:

1. Differential Equations
2. Planar Systems
3. Interacting Species
4. Limit Cycles
5. Hamiltonian Systems, Lyapunov Functions and Stability
6. Bifurcation Theory
7. Three-Dimensional Autonomous Systems and Chaos

Mathematical Modeling:

1. One Variable Optimization
2. Multivariable Optimization
3. Computational Methods for Optimization
4. Introduction to Dynamic Models
5. Analysis of Dynamic Models
6. Simulation of Dynamic Models
7. Probability Models
8. Stochastic Models

Elementary Topology:

1. Set Theory and Logic
2. Topological Spaces and Continuous Functions
3. Connectedness and Compactness
4. Countability and Separation Axioms

Numerical Analysis I:

1. Preliminaries
2. Solutions of Equations in One Variable
3. Interpolation and Polynomial Approximation
4. Numerical Differentiation and Integration
5. Initial-Value Problems for Ordinary Differential Equations
6. Direct Methods for Solving Linear Systems

Number Theory:

1. The Integers
2. Integer Representations and Operations
3. Primes and Greatest Common Divisors
4. Congruences
5. Applications of Congruences
6. Special Congruences
7. Multiplicative Functions
8. Cryptology
9. Primitive Roots

Elementary Real Analysis I:

1. Properties of the Real Numbers
2. Sequences
3. Sets of Real Numbers
4. Continuous Functions
5. Differentiation
6. Integration

Elementary Real Analysis II:

1. Infinite Sums
2. Dense Sets, Oscillation and Continuity on Sets
3. Sequences and Series of Functions
4. Power Series
5. Measure Theory
6. Lebesgue Integration

Even though I've graduated with a math degree, I think I would like to attend school further to pick up Modern Algebra I and II, Complex Analysis, Matrix Theory and maybe one or two more before attempting the math GRE and applying for graduate school. There are many more math classes in the undergraduate program to take, such as History of Mathematics, Boundary Value Problems, Partial Differential Equations, Probability and Statistics II, Numerical Analysis II, Enumeration, Euclidean and Non-Euclidean Geometry and Graph Theory.

I've found a website that aggregates free electronic books in various formats, such as PDF. Tons and tons of mathematics books are referenced to on the site, many of which I've downloaded and begun reading. The site is: http://e-booksdirectory.com/listing.php?category=3. I hope I never lose my passion for