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.

A self-study/reading course in numerical analysis. This course is fairly organized as it will be following the official course syllabus of UC Berkeley's first semester course on numerical analysis, Math 128.

This is a course that will teach about complex numbers and their basic operations before going into quaternions, quaternion operations and eventually quaternionic rotations.

The goal of this course is just to get something out there in the Mathematics section of ureddit that focuses specifically on complex numbers and interests people in complex numbers, as well as hopefully teaching those with a fair bit of knowledge on complex numbers/quaternions something new.

Math is life – everything we do in our day-to-day lives involves math in some way, whether we realize it or not. Graphing trigonometric functions is definitely not an exception, and understanding how to do it will open up a world of graphic solutions, algebraic processes, and even life solutions.

But none of that means anything if you don’t have an easy way of understanding it. That’s where this three-part course comes in.

Introduction – To start things out, I’ll use sample videos and worksheets to give you simple definitions, process outlines, and some basic questions to help you build up an understanding of how to graph trigonometric functions. Even if you’ve tried to learn this before, we’ll start from scratch to get you on the right foot.

Examples – Understanding is all about applying and testing, so next you’ll work through some examples to help drive in what you learned in the first section about graphing trigonometric functions. This isn’t about getting a passing grade, so there’s no stress to get everything right. Complete the whole worksheet if you can, or just pick the problems you know you need to work on, and check your answers against a short step-by-step tutorial that shows you how to get from problem to solution.

Conclusion – Finally, you’ll get another worksheet of questions to discuss, reflect on, and answer to really drive in what you’ve learned and ensure you’ve got it in the long run. For those who want to move on to the next course, there are even challenge problems to get you ready. But mostly, this section is about making sure you’re ready for real-world application, not just finishing a worksheet. It’ll all come together in a final summary video where I point out common mistakes plus tips and little-known tricks to help you along in the future when solving a system of equations graphing.

This course should only take a couple days, but what you learn will help you for the rest of your life. All at a tiny fraction of what a tutor would cost, and right from the comfort of a home laptop, tablet, or phone. No driving, no anxiety, no pressure, all for under $10 with a 30-day money-back guarantee.

See how much simpler math can be. Sign up today to get started!

This course is offered as a traditional lecture series at the Colorado School of Mines. The goal of this University of Reddit course is to leverage its features to facilitate student interaction in an open and easy way. In return for this functionality, I will make available any academic materials created through the course.

** Course Description **

(I, II, S) Classical techniques for first and higher order equations and systems of equations. Laplace transforms. Phase-plane and stability analysis of non-linear equations and systems. Applications from physics, mechanics, electrical engineering, and environmental sciences. Prerequisite: Consent of Department. 3 hours lecture; 3 semester hours.

http://bulletin.mines.edu/undergraduate/programs/engcompsci/ams/#courseinventory

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