Table of Contents
How do I study for pure maths?
If you’re willing to go in head first, get an introductory text book on one of the foundational areas of mathematics, like logic or set theory. Number theory is also a good introduction to pure math. If you want to go the textbook route, I’d recommend The Joy of Sets as a good introductory set theory book.
Is there calculus in pure mathematics?
Pure mathematics became a recognized vocation, achievable through training. The study of functions, called calculus at the first year level becomes mathematical analysis and functional analysis at more advanced levels. Each of these branches of more abstract mathematics have many sub-specialties.
What is the best way to study math for high school?
Study high-school and undergraduate textbooks and do the problems. It may be a good idea to go to an older generation of textbooks since they are less chatty than the current ones. The Chicago Undergradute Mathematics Bibliographyis useful. But don’t obsess too much on which book to read.
What is the first year of an undergraduate mathematics education like?
The first year in an undergraduate mathematics education is primarily about shifting your mindset from the “mechanical” approach taught at highschool/A-Level into the “formal systems” approach that is studied at university. Hence, there is a much more rigourous emphasis on mathematical foundations, including formal descriptions of sets]
Is it possible to self-study university level mathematics?
Self-study of university level mathematics is not an easy task, by any means. It requires a substantial level of discipline and effort to not only make the cognitive shift into “theorem and proof” mathematics, but also to do this as a full autodidact.
What is it like to study mathematics at a university?
At University, mathematics becomes largely about formal systems of axioms and an emphasis on formal proofs. This means that ones thinking is shifted from mechanical solution of problems, utilising a “toolbox” of techniques, towards deep thought about disparate areas of mathematics that can be linked in order to prove results.