# GMU Math Camp (2019)

This will be a short review of main concepts. I mostly draw from these two (online) textbooks:

- Math for CS
- Mathematical methods for economic theory by Martin J. Osborne

## Lecture slides and other materials

### Syllabus.

### Class 1: Communicating Math: Sets, Functions, Relations, Proofs.

### Class 2: Infinitesimals: Real numbers, Calculus, Derivatives, Continuity.

+ A note on CES functions from Norwegian Business School that uses l'Hopital rule
### Class 3: Algebra (updated).

### Class 4: Optimization.

### Class 5: Additional Methods: Diff. eqns, probability spaces.

+ Mathematica notebook with phase diagrams of differential equations
### A small problem set (updated).

## Other materials for independent review

If you were planning to do an independent review, there are plenty of other free PDF textbooks online.

If you are not sure where to begin, picking up any undergrad calc book and solving problems is also a great option.

Personally, I would recommend the following by topic:

- For a quick intro to
**calculus**, I would recommend going through the first two chapters in M.Osbourne's online textbook.
- A heavier
**calculus** option - Vladimir Zorich Mathematical Analysis (Part I) - you can find a pdf copy online.
- For
**Proofs, sets, logic**: Math for CS (chapters 3,4,8 + optionally 10,14,15) (MCS textbook PDF).
- For
**Linear algebra** nothing beats this Youtube channel (seriously, it builds intuition very effectively):
3Blue1Brown.
- For
**Differential equations** a Macro I class handout is usually enough, so I would not worry. But if you are interested, 3Blue1Brown, or any specialized textbooks are also fine, e.g.

Zhang, Wei-Bin. Differential equations, bifurcations, and chaos in economics. Vol. 68. World Scientific Publishing Company, 2005.

To name a few others:

On writing proofs and logic: The Art of Proof: Basic Training For Deeper Mathematics by Matthias Beck and Ross Geoghegan or
A Gentle Introduction to the Art ofMathematics by Joseph Fields

On calculus: Calculus by Gilbert Strang and many many others.