# Undergraduate Mathematics

## What Is This Book For?[edit]

This wikibook is intended as a general overview of undergraduate mathematics. In any one field, it may not have the widest coverage on this wiki but the idea is to present the most useful results with many exercises that are tied in carefully into the rest of the book.

It can be used by readers as a hub to connect their current knowledge to what they want to know, laid out in a traditional textbook style, and for editors as a source to expand out from and create more specific titles.

The project was inspired by the *Feynmann Lectures in Physics* which feature as recommended reading below, for mathematical physicists. It also owes a debt to the early success of Linear Algebra.

## Before We Begin[edit]

We expect that the reader have the level usually required of a student starting a university level course that heavily involves mathematics. For example in the UK an A level equivalent is required.

Specifically it would be useful to know skills like this:

- Be able to perform basic arithmetic with real numbers
- Be able to find roots of polynomials
- Know the basic meaning of terms like
*function*and*set* - Be able to roughly sketch simple graphs without plotting large numbers of points
- Know how to differentiate simple functions with the Sum, Product, Chain and Quotient rules
- Know how to integrate simple functions by parts and by substitution
- Be able to use either a scientific hand calculator or an equivalent computer program

If you follow the material in this wikibook, then find yourself stuck not knowing a method we assumed, please try looking for a work in K12 to give you the right skill.

### Contents[edit]

Typically larger courses, such as real analysis, are 20 credit courses in the 360 credit breakdown of an undergraduate degree. So it should not be assumed that all courses are the same in scale. Most courses are assumed to be 10 credit courses but more material may be included to help cover the different course structures internationally.

## First Year Courses[edit]

- The Meaning and Methods of Proof
- Introduction to Newtonian Mechanics
- Introduction to Statistics
- Multivariate Calculus
- Introduction to Linear Algebra
- Introduction to Mathematical Programming
- Real Analysis (20 Credits)
- The History of Mathematics

## Second Year Courses[edit]

- Introduction to the Theory of Groups
- Non-Euclidean Geometry
- Ordinary Differential Equations
- Discrete Mathematics
- Point-Set Topology
- Number Theory
- Mathematical Biology
- Mathematical Physics

## Third and Fourth Year Courses[edit]

- The Group Theory of the Symmetries of Simple Shapes
- Advanced Statistics
- Complex Analysis
- Algebraic Topology
- Representation Theory
- Cryptography