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Do you mind sharing the books you found helpful to self learn math with a tutor? I am looking to also go on a self study mathematical journey

by zd123 5y ago

deleted 5y ago
[deleted]
cg30e 5y ago
For sure. I'll list some books for introduction to proofs, abstract algebra, real analysis, topology and category theory. These are not comprehensive, just listing books off the top of my head. I'll definitely be leaving off personal favorites other people have. You'll like some better than others. Some of these are beginner books and some are more advanced. A good tutor can help you get through the more advanced books. I tried to list the most beginner friendly book first in the list under each subject. Then the more advanced books later in the list. Introduction to Proofs: Just pick one of these that speaks to you the most. All three are good. Discrete Mathematics with Applications - Epp Discrete Mathematics and Its Applications - Rosen Mathematical Proofs: A Transition to Advanced Mathematics - Chartrand, et al. Abstract Algebra: How to Think about Abstract Algebra - Alcock Abstract Algebra - Pinter Abstract Algebra: A First Course - Saracino Algebra - Artin Abstract Algebra - Herstein Abstract Algebra - Dummit & Foote Linear Algebra: Maybe an engineering based book first if you haven't seen linear algebra in a while (e.g. Strang or Linear Algebra: Step by Step by Singh). Then: Linear Algebra - Friedberg, et al Linear Algebra Done Right - Axler Linear Algebra - Hoffman & Kunze Real Analysis: How to Think About Analysis - Alcock Understanding Analysis - Abbott Tao's Analysis text Principles of Mathematical Analysis - Rudin Topology: Topology - Munkres Topology A Categorical Approach - Tai-Danae Bradley, Tyler Bryson, and John Terilla Check out this list: http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf for others. Category theory: Categories and Toposes: Visualized and Explained - Southwell Conceptual Mathematics: A First Introduction to Categories - Lawvere Category Theory for Programmers - Milewski (if you like functional programming) Programming with Categories - Fong, Milewski, Spivak (if you like functional programming) Category Theory in Context - Riehl There are a few others by Spivak which you may like. If you don't know category theory whatsoever then I like Southwell the best (pair them up with his youtube videos). Eugenia Cheng also has a nice set of lecture videos. If you already know math pretty well, then Riehl is a favorite. Hope that helps!
- laichzeit0 5y ago
  I see you did a lot of analysis, but no Calculus, why is that?
  - mden 5y ago
    Calculus is a subset of analysis. It's not really its own subject. Generally what people call calculus is a collection of results that are part of analysis.

Do you mind sharing the books you found helpful to self learn math with a tutor? I am looking to also go on a self study mathematical journey

by zd123 5y ago

Do you mind sharing the books you found helpful to self learn math with a tutor? I am looking to also go on a self study mathematical journey

deleted 5y ago

[deleted]

cg30e 5y ago

For sure. I'll list some books for introduction to proofs, abstract algebra, real analysis, topology and category theory. These are not comprehensive, just listing books off the top of my head. I'll definitely be leaving off personal favorites other people have. You'll like some better than others. Some of these are beginner books and some are more advanced. A good tutor can help you get through the more advanced books. I tried to list the most beginner friendly book first in the list under each subject. Then the more advanced books later in the list. Introduction to Proofs: Just pick one of these that speaks to you the most. All three are good. Discrete Mathematics with Applications - Epp Discrete Mathematics and Its Applications - Rosen Mathematical Proofs: A Transition to Advanced Mathematics - Chartrand, et al. Abstract Algebra: How to Think about Abstract Algebra - Alcock Abstract Algebra - Pinter Abstract Algebra: A First Course - Saracino Algebra - Artin Abstract Algebra - Herstein Abstract Algebra - Dummit & Foote Linear Algebra: Maybe an engineering based book first if you haven't seen linear algebra in a while (e.g. Strang or Linear Algebra: Step by Step by Singh). Then: Linear Algebra - Friedberg, et al Linear Algebra Done Right - Axler Linear Algebra - Hoffman & Kunze Real Analysis: How to Think About Analysis - Alcock Understanding Analysis - Abbott Tao's Analysis text Principles of Mathematical Analysis - Rudin Topology: Topology - Munkres Topology A Categorical Approach - Tai-Danae Bradley, Tyler Bryson, and John Terilla Check out this list: http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf for others. Category theory: Categories and Toposes: Visualized and Explained - Southwell Conceptual Mathematics: A First Introduction to Categories - Lawvere Category Theory for Programmers - Milewski (if you like functional programming) Programming with Categories - Fong, Milewski, Spivak (if you like functional programming) Category Theory in Context - Riehl There are a few others by Spivak which you may like. If you don't know category theory whatsoever then I like Southwell the best (pair them up with his youtube videos). Eugenia Cheng also has a nice set of lecture videos. If you already know math pretty well, then Riehl is a favorite. Hope that helps!

laichzeit0 5y ago
I see you did a lot of analysis, but no Calculus, why is that?
- mden 5y ago
  Calculus is a subset of analysis. It's not really its own subject. Generally what people call calculus is a collection of results that are part of analysis.