What Are Some Recommended Post A-Level Mathematics Topics?

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SUMMARY

The discussion centers on recommended post A-Level mathematics topics for individuals with a background in A-Level mathematics and quantum mechanics. Key areas of interest include algebraic topology, number theory, polynomials, and group theory. Participants suggest exploring introductory books on these subjects, while also mentioning Euclid's Elements as a foundational text for various mathematical concepts. The focus is on advancing mathematical knowledge beyond differential equations.

PREREQUISITES
  • A-Level Mathematics proficiency
  • Basic understanding of quantum mechanics
  • Familiarity with differential equations
  • Interest in advanced mathematical concepts
NEXT STEPS
  • Research introductory texts on algebraic topology
  • Explore number theory resources, such as "An Introduction to the Theory of Numbers" by G.H. Hardy and E.M. Wright
  • Study group theory through "A Book of Abstract Algebra" by Charles Pinter
  • Read Euclid's Elements for foundational insights into geometry and mathematical reasoning
USEFUL FOR

Mathematics enthusiasts, students transitioning from A-Level to university-level mathematics, and anyone interested in exploring advanced topics such as algebraic topology and number theory.

moriheru
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I have did my A-level mathematics a long while ago and I did QM for about three to four months and got to Bosonic String theory now, but I would like to do some mathematics beside String theory. I do not know if differential equations are coverd in university but I did them to and I know how to solve them, so please do not suggest books on differential equations. My question is where to go from here. The fields that apeal to me are algebraic topology, number theory, polynomials, group theory. Any introductiory books on these fields or any other post A-level books are welcome.

Thanks for any help.
 
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