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Oh man, I can totally relate. I'm a self-taught programmer, and have been trying to learn math in the same way for the past couple of years. I've certainly im

Oh man, I can totally relate. I'm a self-taught programmer, and have been trying to learn math in the same way for the past couple of years. I've certainly improved a little bit, but learning math is very different from learning programming, and I'm frustrated. Every time I buy a book, I think I understand what I'm reading until the time comes to do the problems ... then I get hopelessly stuck and discouraged. I've never encountered something I couldn't learn with a bit of consistent effort before. To make matters worse, I can already appreciate the beauty of math from a distance, yet it somehow remains totally inaccessible to me, and this despite my honest-to-god best efforts. I don't know what I'm doing wrong. It's a terrible feeling. =( I harbor a secret fantasy of meeting a maths enthusiast who would take me under his or her wing, and help me struggle through problems for one hour each week.

akomtu 5y ago
The secret trick is proving theorems. Prove the Pythagoras theorem or prove that quick sort is indeed a NlogN algorithm (the latter needs some real math skills). A proof counts only when you can explain even the most boring detail in the proof. Books on math only tell what proofs and in what order you need to learn. I'd compare math proofs to functions, and understanding of math is a lot like understanding how complex functions work down to assembly level.
tarentel 5y ago
Maybe try different maths. I majored in math in college and even though I have a degree I would say I am pretty terrible at it. Some areas I understood almost immediately at least at the lower levels I took them such as algebra and combinatorics, but real analysis after like basic limits completely eludes me.
buescher 5y ago
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."
mathgenius 5y ago
What kind of mathematics have you been trying to learn?
albrewer 5y ago
Paul Dawkins has combined his 25 years of experience of teaching and turned his daily lecture plans into textbooks on the subjects he teaches (Algebra, Calc 1, 2, 3, and differential equations). These are the most approachable math texts I've ever found. https://tutorial.math.lamar.edu/ https://tutorial.math.lamar.edu/
- omginternets 5y ago
  Thanks, I really appreciate it! I'll take a look at these tonight.
fleetwoodsnack 5y ago
I love the following quote from Andrew Wiles: "Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room." I find this rings true--I didn't really understand the purpose of some of the material in differential calculus (Calc I) until I studied integral calculus (Calc II), and I didn't understand some of the material in integral calculus (II) until I took multivariable calculus (Calc III). Funnily enough, it was only after taking a combination of real analysis and discrete math (two years into undergraduate studies) that I finally had the A-ha moment when my real analysis class taught me how to actually read and write proofs, and my discrete math class finally made sets clear. THEN Calculus's proofs and its set-based conditions finally made sense. I could go on, but there's really something to the frustration that beginners in math have. It's ironical, but the best way to learn calculus is reproducing calculus's underlying proofs; but at the same time, the best way to learn how to read and write proofs is to use calculus as an example of a system you already know intuitively, and just need to learn the formal language of proofs to explain it. I guess my point is that there are genuine structural challenges/interactions in math's component knowledge systems which make the difficulty of learning math natural, if not to be expected. All of this to say, chin up lads, the only way out is through, and sometimes you're running blind. But that's okay, Andrew Wiles did too and he proved Fermat's Last Theorem.
- omginternets 5y ago
  Thank you for the kind encouragement. Believe it or not, it's quotes like these that form my last line of defense against permanent discouragement. In truth, I'm not interested in math because it's easy, but because it's hard. I just wish I could consistently make some progress, even if it's small. Ah well, no use raging against reality.
- jeffwass 5y ago
  Great quote. For me, as a physics major, calculus didn’t “click” until I had to use it for solving physics problems.

akomtu 5y ago

The secret trick is proving theorems. Prove the Pythagoras theorem or prove that quick sort is indeed a NlogN algorithm (the latter needs some real math skills). A proof counts only when you can explain even the most boring detail in the proof. Books on math only tell what proofs and in what order you need to learn. I'd compare math proofs to functions, and understanding of math is a lot like understanding how complex functions work down to assembly level.

tarentel 5y ago

Maybe try different maths. I majored in math in college and even though I have a degree I would say I am pretty terrible at it. Some areas I understood almost immediately at least at the lower levels I took them such as algebra and combinatorics, but real analysis after like basic limits completely eludes me.

buescher 5y ago

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."

mathgenius 5y ago

What kind of mathematics have you been trying to learn?

albrewer 5y ago

Paul Dawkins has combined his 25 years of experience of teaching and turned his daily lecture plans into textbooks on the subjects he teaches (Algebra, Calc 1, 2, 3, and differential equations). These are the most approachable math texts I've ever found. https://tutorial.math.lamar.edu/ https://tutorial.math.lamar.edu/

omginternets 5y ago
Thanks, I really appreciate it! I'll take a look at these tonight.

fleetwoodsnack 5y ago

I love the following quote from Andrew Wiles: "Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room." I find this rings true--I didn't really understand the purpose of some of the material in differential calculus (Calc I) until I studied integral calculus (Calc II), and I didn't understand some of the material in integral calculus (II) until I took multivariable calculus (Calc III). Funnily enough, it was only after taking a combination of real analysis and discrete math (two years into undergraduate studies) that I finally had the A-ha moment when my real analysis class taught me how to actually read and write proofs, and my discrete math class finally made sets clear. THEN Calculus's proofs and its set-based conditions finally made sense. I could go on, but there's really something to the frustration that beginners in math have. It's ironical, but the best way to learn calculus is reproducing calculus's underlying proofs; but at the same time, the best way to learn how to read and write proofs is to use calculus as an example of a system you already know intuitively, and just need to learn the formal language of proofs to explain it. I guess my point is that there are genuine structural challenges/interactions in math's component knowledge systems which make the difficulty of learning math natural, if not to be expected. All of this to say, chin up lads, the only way out is through, and sometimes you're running blind. But that's okay, Andrew Wiles did too and he proved Fermat's Last Theorem.

omginternets 5y ago
Thank you for the kind encouragement. Believe it or not, it's quotes like these that form my last line of defense against permanent discouragement. In truth, I'm not interested in math because it's easy, but because it's hard. I just wish I could consistently make some progress, even if it's small. Ah well, no use raging against reality.
jeffwass 5y ago
Great quote. For me, as a physics major, calculus didn’t “click” until I had to use it for solving physics problems.