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Algebra Calculus is an interesting topic to both the student who enrolls in the course and the teacher or professor teaching the course. This is a unique level of mathematics that has become notably consistent. In the first year courses of algebra and calculus the demand that students understand a different number systems and geometric properties as well as model mathematics problems and solve algebraic equations. On balance, applications to physics have done more to advance this form of science through abstract mathematics than pure mathematics research. This is a more advanced course and will require dedication on the part of the student, but the rewards and knowledge to adversely gain in the end will most certainly last a lifetime. This is the type of course that when compounded by the previous required mathematics courses will open up many prominent doors for later employment. It is a fascinating and rewarding career in the world of mathematics and science.
Papers with extensions and improvements in the calculus are collections in Universal Geometric Calculus. With general arguments and many fine, explicit examples, the case made there and elsewhere that geometric algebra is a more efficient general computational tool than matrix algebra. Geometric Calculus is a candidate to supplant or subsume matrix algebra in computer software and software designs for scientific computation. The use of geometric algebra in computer aided geometric design, computer vision and robotics is expanding very rapidly.
The most comprehensive treatment of the mathematical theory is through the writing in the Clifford Algebra to Geometric Calculus. This is one of the books that the student will most likely examine and walk away upon the completion of the course with a full understanding of the mysterious workings.
The applications of the physics are now so diverse and extensive that there is a need to organize them in books for greater accessibility for the student and the teacher or professor. In the meantime, the various web sites serve the function in the form of on line research and easily accessible books. These are the only sites expressly concerned with the development of a universal specific calculus. The most exciting developments are in relativistic quantum mechanics and gravitation theory where studies brought creative and innovative insights and simplifications.