What are some branches one is introduced to as undergraduate?

Question

I just completed my high school and have little knowledge about what an undergraduate math program includes. I wanted to know what are various branches of mathematics one is introduced to as an undergraduate. I know some like real analysis, linear algebra and abstract algebra. If possible do recommend some textbooks too.

Answer 1

You should take a look at "How to Become a (Pure) Mathematician" though you should be aware in advance that

1. not everybody studies everything on that list,
2. not everybody studies the topics listed in the order listed, and
3. the "stages" listed only loosely correspond to years in a degree course.

Note also that the site takes inspiration from Gerard t'Hooft's site, which is to do with physics. It may be of interest to you to keep an eye on physics as well; the subject provides motivation and applications for much of undergraduate mathematics.

Answer 2

The Main ones are probably caculus, anaysis, diferential equations and abstract algebra.

Answer 3

Linear algebra:(if you have no prior experience then the first course will likely cover things like linear equations , matrices and and some basic vector geometry ) and then vector spaces , linear transformations , eigenvalues , inner product spaces

Calculus: ( the content in each course may not be the same depending on where you study) starting with calculus 1 if you haven't which usually focuses on limits and derivatives and their applications such as related rates , calculus 2 which usually focuses on integration , different coordinate systems and applications such as volume of surfaces of revolutions and calculus 3 which is usually a first course in multivariable calculus ie partial derivatives , multiple integrals Then calculus "4" or advanced calculus which covers topics like line integrals and vector operators , such as gradient , curl and divergence Ordinary Differential equations and at a higher level partial differential equations

Analysis: a more rigorous view of calculus with proving results related to continuity , differentiability , more on sequences and series ( also in calculus), in later courses more on the Riemann integral, metric spaces , point set topology .

Abstract Algebra: more on sets , groups, fields , rings ( algebraic structures ).

And of course there is probability and statistics , logic , complex variables and analysis , mathematical physics , and much more .