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My suggestions for new University math faculty courses

Actual courses

You can start teach these courses in your University immediately (as facultative disciplines):

Category of Endomorphisms and Pseudomorphisms

I advise to add this course to obligatory program of abstract mathematics and computer science faculties, as a sub-course of the category theory course. For math students of other specializations I also recommend to study this topic at least partially.

It is especially important for students of Math Logic and Computer Science, and also important for algebraists, as well as other math students.

This free online text quite suits to be used as the studybook.

Future courses

These disciplines are not yet completely developed but indeed are to be added to the education programs in the future when they will be completely developed:

Axiomatic/Algebraic Theory of Formulas (Expressions)

Algebraic theory of expressions should be added to programs of all math and computer science faculties of all Universities. However dependently on specialization it may be taught in more or less volume and depth.

It is especially important for students specializing in Math Logic, Theoretical Computer Science (as well as for advanced programmers), and Abstract Algebra.

Theory of Formulas should be a separate discipline (however it alternatively may be taught as a part of Category Theory or Abstract Algebra courses).

Theory of Formulas is a relatively big but very important topic for a modern mathematician or computer scientist. So this course should probably pull out some older course from University program.

Theory of Dependencies and Theory of Constructs

I recommend to teach it as a part of the Theory of Formulas course (see above).

21 Century Math Method (21MM)

See Pedagogical aspects of 21 Century Math Method.

Probably this should be taught even to children (on examples).

Volunteering

You can volunteer to develop these courses (by writing education programs, exam questionnaires, course descriptions, etc.) by online editing Victor Porton Math Courses at my personal Wiki.

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