Group representations are where group theory meets linear algebra, and important applications arise in various math subjects (number theory, analysis, algebraic geometry), physics, and chemistry.

We consider the basic representation theory of finite groups. Goals include a look at Fourier series/analysis using groups and elementary character theory.

Category theory is a branch of mathematics that emerged in the 1950s to understand how the different areas of mathematics relate to each other. Today, its influence pervades nearly all of mathematics, in addition to being an important area of study in its own right. This course will cover the basic concepts of category theory, with an emphasis on intuition and examples.

The art and science of cryptography - from prehistoric through moderns times. Includes video & interactive exercises. posted on Khan Academy

This epic journey will take us from smoke signals to internet compression and the modern day search for extraterrestrial intelligence. posted on Khan Academy

I really enjoyed Modern Algebra, so much so that I decided to make a lecture series explaining all the different topics via examples, proofs, and fun pieces of insight.

This course will cover what is normally covered in two full years of Algebra 1 & Algebra 2. This course will prepare you very well for pre-calculus and topics later on.

This course teaches the number systems, properties of real numbers, functions, limits, continuity, differentiation and its applications, integration, and the fundamental theorem of calculus.

Non-bankers can learn to understand the mathematical models that have made the headlines so many times in recent years. A course for students of economics, business studies, mathematics, physics and computer science. In this course you will simulate the time evolution of prices of financial assets, use the Black-Scholes model to price European or Asian options and compute the Value-at-Risk of a portfolio. The approach is hands-on with a strong emphasis on practical simulations that you will program, run and explore in your own computer.

"Monte Carlo Methods in Finance" will be offered on iversity from 20 January, 2014 until 16 April, 2014.

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