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I am not a mathematician or math teacher and I would not call myself a maths enthusiast, but what were you trying to learn? For the usual undergraduate courses

I am not a mathematician or math teacher and I would not call myself a maths enthusiast, but what were you trying to learn? For the usual undergraduate courses, there are Schaum's outlines, which are cheap and usually OK for self-study. There are also explanatory books that you might find helpful, that might not form a whole substitute for a textbook - an example would be Div, Grad, Curl, and All That for vector calculus. It's a bit of a trick to find them on Amazon and through other searches, but you can get practiced at it.

omginternets 5y ago
Broadly speaking, I've been approaching mathematics from two different angles: CS, and the mathematical background that subtends it. On the CS front, I'm interested in two main subjects: - Distributed Systems (especially peer-to-peer overlays) - Programming Language Design (in particular: type theory, algebraic effects, and -- more recently -- optimal beta reduction) On the pure math side, I've tried to focus my efforts on topics related to the above. I've tried working through "introductory" books on each of the following subjects: - Combinatorics - Graph Theory - Category Theory Prior to that, I tried working through some more general books. This is where most of my small progress emerged: - Thompson's Calculus Made Easy - Stewart and Tall's The Foundation of Mathematics (Set Theory) In all cases, the biggest blocker for me is the proofs and exercises. I rapidly get stuck on a problem, which of course prevents me from understanding the subsequent chapters.
- buescher 5y ago
  What Schaum's Outlines would be relevant here?
  - omginternets 5y ago
    Just ordered Schaum's Outline on Graph Theory. Thank you for the recommendation!
    - buescher 5y ago
      I didn't find it, you did!
  - Dalrymple 5y ago
    The Schaum's book of most interest to the original poster (Abigail Rabieh)is the following: Schaum's 3000 Solved Problems in Linear Algebra by Seymour Lipschutz. Below is a precis: "Master linear algebra with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests; Study quickly and more effectively; Learn the best strategies for solving tough problems in step-by-step detail; Get the big picture without spending hours pouring over long textbooks. Review what you've learned in class by solving thousands of relevant problems that test your skill. Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams. Inside you will find: 3000 solved problems with complete solutions--the largest selection of solved problems yet published on linear algebra; A superb index to help you quickly locate the types of problems you want to solve; Problems like those you'll find on your exams; Techniques for choosing the correct approach to problems; Guidance on choosing the quickest, most efficient solution. If you want top grades and thorough understanding of linear algebra, this powerful study tool is the best tutor you can have! Chapters include: Vectors in R" and C." Matrix Algebra. Systems of Linear Equations. Square Matrices.Determinants. Algebraic Structures. Vector Spaces and Subspaces. Linear Dependence, Basis, Dimension. Mappings. Linear Mappings. Spaces of Linear Mappings. Matrices and Linear Mappings. Change of Basis, Similarity. Inner Product Spaces, Orthogonality. Polynomials over a Field. Eigenvalues and Eigenvectors, Diagonalization. Canonical Forms. Linear Functionals and the Dual Space. Bilinear, Quadratic, and Hermitian Forms. Linear Operators on Inner Product Spaces. Applications to Geometry and Calculus."
- arghnoname 5y ago
  Proofs are the great 'leveling-up' of mathematics. At my former university they had a bridge class for students to take when they made the leap from more mechanistic mathematics to proofs. I didn't have the benefit of taking it when I was a math major (to my regret, it was painful to level-up), but it looks like the text they use is publicly available: http://www2.math.umd.edu/~shalper/text.pdf http://www2.math.umd.edu/~shalper/text.pdf
  - omginternets 5y ago
    Many thanks! Proofs are something I've always struggled with, having never been taught any methodology. I've added this to my reading list.
    - graycat 5y ago
      The proofs in standard Euclidean high school plane geometry are a perfectly good introduction to how to write proofs. A good next step is just a college course in abstract algebra -- sets, groups, rings, fields, prime numbers, the fundamental theorem of arithmetic, the fundamental theorem of algebra, Galois theory (why with Euclidean construction it is impossible to construct a square with the same area as a given circle), why the square root of 2 is irrational, the Euclidean greatest common divisor algorithm, the Chinese remainder theorem, vector spaces, .... Here there are essentially no prerequisites. The results proved in an abstract algebra course are often just embarrassingly childishly simple so that getting a solid proof is easy. For the issue of writing style for proofs, just pick that up from the text. E.g., usually say since instead of because. The proofs in abstract algebra and, really, the rest of math, are really essentially the same as in high school plane geometry but just written in a less rigid style. If want a theorem proving course in calculus, first take calculus where theorem proving is not the main content, then take abstract algebra (where will use no calculus), and then take a theorem proving course in calculus, e.g., from W. Rudin, Principles of Mathematical Analysis. With this sequence, should never be without prerequisites or in doubt about the reason, point, value, or intuitive view of the material. Yes, the Wiles quote is really good for describing research, but learning need be nowhere nearly that challenging.
- ColinWright 5y ago
  The stuff I've done is 40 years ago now, but I've done some combinatorics and some graph theory. It's been so long that it's possible that I can't help you at all, but I might be able to talk in generalities, and maybe that's all you need. My email is in my profile.
  - omginternets 5y ago
    Thank you so much - you have no idea how much this means to me. I'll be sure to shoot you an email next time I get stuck, which will happen more or less as soon as I decide to try again :'D
    - ColinWright 5y ago
      Well, as I say, I may not be of any help, but at least you'll have someone with whom to share your confusion. I'll look for your email.

omginternets 5y ago

Broadly speaking, I've been approaching mathematics from two different angles: CS, and the mathematical background that subtends it. On the CS front, I'm interested in two main subjects: - Distributed Systems (especially peer-to-peer overlays) - Programming Language Design (in particular: type theory, algebraic effects, and -- more recently -- optimal beta reduction) On the pure math side, I've tried to focus my efforts on topics related to the above. I've tried working through "introductory" books on each of the following subjects: - Combinatorics - Graph Theory - Category Theory Prior to that, I tried working through some more general books. This is where most of my small progress emerged: - Thompson's Calculus Made Easy - Stewart and Tall's The Foundation of Mathematics (Set Theory) In all cases, the biggest blocker for me is the proofs and exercises. I rapidly get stuck on a problem, which of course prevents me from understanding the subsequent chapters.

buescher 5y ago
What Schaum's Outlines would be relevant here?
- omginternets 5y ago
  Just ordered Schaum's Outline on Graph Theory. Thank you for the recommendation!
  - buescher 5y ago
    I didn't find it, you did!
- Dalrymple 5y ago
  The Schaum's book of most interest to the original poster (Abigail Rabieh)is the following: Schaum's 3000 Solved Problems in Linear Algebra by Seymour Lipschutz. Below is a precis: "Master linear algebra with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests; Study quickly and more effectively; Learn the best strategies for solving tough problems in step-by-step detail; Get the big picture without spending hours pouring over long textbooks. Review what you've learned in class by solving thousands of relevant problems that test your skill. Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams. Inside you will find: 3000 solved problems with complete solutions--the largest selection of solved problems yet published on linear algebra; A superb index to help you quickly locate the types of problems you want to solve; Problems like those you'll find on your exams; Techniques for choosing the correct approach to problems; Guidance on choosing the quickest, most efficient solution. If you want top grades and thorough understanding of linear algebra, this powerful study tool is the best tutor you can have! Chapters include: Vectors in R" and C." Matrix Algebra. Systems of Linear Equations. Square Matrices.Determinants. Algebraic Structures. Vector Spaces and Subspaces. Linear Dependence, Basis, Dimension. Mappings. Linear Mappings. Spaces of Linear Mappings. Matrices and Linear Mappings. Change of Basis, Similarity. Inner Product Spaces, Orthogonality. Polynomials over a Field. Eigenvalues and Eigenvectors, Diagonalization. Canonical Forms. Linear Functionals and the Dual Space. Bilinear, Quadratic, and Hermitian Forms. Linear Operators on Inner Product Spaces. Applications to Geometry and Calculus."
arghnoname 5y ago
Proofs are the great 'leveling-up' of mathematics. At my former university they had a bridge class for students to take when they made the leap from more mechanistic mathematics to proofs. I didn't have the benefit of taking it when I was a math major (to my regret, it was painful to level-up), but it looks like the text they use is publicly available: http://www2.math.umd.edu/~shalper/text.pdf http://www2.math.umd.edu/~shalper/text.pdf
- omginternets 5y ago
  Many thanks! Proofs are something I've always struggled with, having never been taught any methodology. I've added this to my reading list.
  - graycat 5y ago
    The proofs in standard Euclidean high school plane geometry are a perfectly good introduction to how to write proofs. A good next step is just a college course in abstract algebra -- sets, groups, rings, fields, prime numbers, the fundamental theorem of arithmetic, the fundamental theorem of algebra, Galois theory (why with Euclidean construction it is impossible to construct a square with the same area as a given circle), why the square root of 2 is irrational, the Euclidean greatest common divisor algorithm, the Chinese remainder theorem, vector spaces, .... Here there are essentially no prerequisites. The results proved in an abstract algebra course are often just embarrassingly childishly simple so that getting a solid proof is easy. For the issue of writing style for proofs, just pick that up from the text. E.g., usually say since instead of because. The proofs in abstract algebra and, really, the rest of math, are really essentially the same as in high school plane geometry but just written in a less rigid style. If want a theorem proving course in calculus, first take calculus where theorem proving is not the main content, then take abstract algebra (where will use no calculus), and then take a theorem proving course in calculus, e.g., from W. Rudin, Principles of Mathematical Analysis. With this sequence, should never be without prerequisites or in doubt about the reason, point, value, or intuitive view of the material. Yes, the Wiles quote is really good for describing research, but learning need be nowhere nearly that challenging.
ColinWright 5y ago
The stuff I've done is 40 years ago now, but I've done some combinatorics and some graph theory. It's been so long that it's possible that I can't help you at all, but I might be able to talk in generalities, and maybe that's all you need. My email is in my profile.
- omginternets 5y ago
  Thank you so much - you have no idea how much this means to me. I'll be sure to shoot you an email next time I get stuck, which will happen more or less as soon as I decide to try again :'D
  - ColinWright 5y ago
    Well, as I say, I may not be of any help, but at least you'll have someone with whom to share your confusion. I'll look for your email.