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Algebra I and Algebra II studiy the basic forms of algebra, including vector spaces, symmetry groups, bilinear forms, linear transformations, linear groups for the first class and ideals, fields, modules, factorization, polynomial rings, field extensions, integers in quadratic number fields, and Galois theory in the second course. Once you're finished, you should know the fundamentals of the algebraic math used for so many other studies in mathematics. Both these courses are free online college courses from MIT. Introduction to Calculus is MIT's basic introduction to calculus. You'll use video lectures, assignments, solutions, lecture notes, and exams to master this material. Principles of Applied Mathematics shows not just math used in a classroom or laboratory setting, but math used to solve real world problems. Examples are included from various natural phenomena and use partial differential equations. In fact, the course could be described as a study of PDEs. The problems solved come from a wide range of fields, including physics, biology, complex systems, and chemistry. The mathemetical challenges you'll face include chemical reactions, heat transfer, pattern formation, population dynamics, shock waves, bio-fluid flows, diffusion, traffic flows, and hydraulic jumps. Geometry and Quantum Field Theory allows you to study QFT using mathemetical language. You'll study classic field theory, Feynman diagrams, and free quantum theories. This is a rigorous course, but still considered an undergraduate class. When you're finished, you should be able to understand papers and lectures presented at seminars for Quantum Field Theory and String Theory. ## MIT Free Math Classes - OpenCourseWareThe OpenCourseWare program from the Massachusettes Institute of Technology is the world's best for free distance learning courses. Since it's MIT behind the program, you know it's going to have a huge number of science, technology, and mathematics courses offered. The material covered is from past semesters at MIT, usually sometime from 2001 to 2011, so you're being exposed to the same subject matter, lectures, and study materials that MIT students studied. Since the list is huge, I wanted to link to as many of them as possible, both to give you an idea of the potential classes available and to give you a full range of choices. Look on the MIT Open Sourceware site for even more free online mathematics classes. - Linear Algebra
- Mathematics for Computer Science
- Advanced Calculus for Engineers
- Mathematical Exposition
- Street-Fighting Mathematics
- Non-Linear Dynamics I: Chaos
- Theory of Computation
- Advanced Topics in Cryptography
- Quantum Computation
- The Art of Counting
- Simplicity Theory
If you want to study mathematics seriously and not pay a dime for your studies, you won't find a better source of education than the MIT OpenCourseWare. You can study a huge range of math topics and transform yourself into an advanced mathematician if you have the time, dedication, and mathematical aptitude to use this distance learning program. |