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What are Some Courses Not Usually Taught in Undergrad but Should Be in Today's Time
Some of my course ideas are (these may be taught in your country/institute but not in mine, so your list may vary):
- Lattice and Order Theory (Kind of sad it is often relegated as a afterthought in combinatorics courses where only a few results on chains and antichains like Dilworth's theorem are discussed)
- Commutative and Homological Algebra (I find it very dissatisfactory where my institute offers courses in algebraic geometry and algebraic number theory but don't teach this course)
- Category Theory (This one really hurts, as not only ideas of category permeate through abstract algebra and computer science, but they also take one to the fundamentals of set theory and push its limitations for undergrads to see why an axiomatically defined set theory is important)
- Introduction to Mathematical Logic (Needs no explanation as the mathematical institutes in my country have relegated such a beautiful and omnipresently inportant subject like logic as an afterthought)
- Operator Algebras (Logical next step after studying functional analysis as topological vector spaces like Hilbert, Banach and Sobolev spaces arise in many branches of mathematics and physics)
- Design Theory and Matroids (Very useful for anybody going into combinatorics)
#science
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Some of my course ideas are (these may be taught in your country/institute but not in mine, so your list may vary):
- Lattice and Order Theory (Kind of sad it is often relegated as a afterthought in combinatorics courses where only a few results on chains and antichains like Dilworth's theorem are discussed)
- Commutative and Homological Algebra (I find it very dissatisfactory where my institute offers courses in algebraic geometry and algebraic number theory but don't teach this course)
- Category Theory (This one really hurts, as not only ideas of category permeate through abstract algebra and computer science, but they also take one to the fundamentals of set theory and push its limitations for undergrads to see why an axiomatically defined set theory is important)
- Introduction to Mathematical Logic (Needs no explanation as the mathematical institutes in my country have relegated such a beautiful and omnipresently inportant subject like logic as an afterthought)
- Operator Algebras (Logical next step after studying functional analysis as topological vector spaces like Hilbert, Banach and Sobolev spaces arise in many branches of mathematics and physics)
- Design Theory and Matroids (Very useful for anybody going into combinatorics)
#science
source
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