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Do the exercises have solutions? The most annoying things about math books is the lack of solutions. A beginner absolutely needs to know whether or not their so

Do the exercises have solutions? The most annoying things about math books is the lack of solutions. A beginner absolutely needs to know whether or not their solutions are correct. The “the reader should know if they are correct” logic doesn’t apply here. A beginner could easily have faulty logic and fool themselves into thinking their solutions are correct. I usually don’t buy math books without solutions if I’m self-studying. Would like to know if solutions are provided in this book. If not, I won’t consider buying it. If this book doesn’t make the cut with a solution manual, does anyone have recommendations on an intro to proofs book with one?

Koshkin 8y ago
Agree. Actually, studying a good solution even if you have one of your own is one of the best ways to learn mathematical tricks of the trade, so to speak - just as it's a great way to learn coding: one learns from the master (as one should) and not just "from the book."
- chii 8y ago
  being told a solution can sometimes lead to "rote" learning - where you learn a particular way of solving the problem, rather than applying creative thinking. Also, if you can't prove a solution correct, then you haven't solved it!
  - ptd 8y ago
    Is this a feature or a bug? If it takes you two weeks to apply creative solutions and it take me one week to apply a “rote” solution, what is the benefit?
    - gbear605 8y ago
      The idea is that it might take you longer to learn, but when you are applying it in the real world and hit real world problems that are messy, you’ll be a lot faster
      - ptd 8y ago
        That’s the idea. In practice does it actually work out like that?
    - username90 8y ago
      The main reason to study mathematics is to build and fix your intuition, hence studying rote solutions is a waste of time. It might help you pass the class but it wont help you much at all in other parts of life. For example, at work nobody will care if you have rote memorized a solution or not since they will have already done the math, you will just apply formulas others have came up with. In order to do anything important with the math (not just solving school problems) you need to have intuition for it.
      - threwythrw 8y ago
        I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct. True beginners may think they have solid intuition and a rigorous proof, but without outside validation, may have a blantant or subtle error they cannot see. The point is not to study rote solutions, but to check correctness. Edit: To your reply below, I’m talking about someone that is self-studying and has no access to a teacher. The suggestion the beginner (without a teacher) should “know” whether or not their solutions are correct is something I disagree with. I do agree with there are multiple ways to prove something and such a beginner may think their proof is incorrect based on a provided solution, when it may be correct, just different. This is why an instructor is valuable.
        username90 8y ago
        > I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct. Yes, which is why you want a teacher until you reach that stage. > The point is not to study rote solutions, but to check correctness. Looking at others solutions can in no way prove that your solution is incorrect so I am not sure how those would help you. However having access to others solutions often makes students doubt their own solutions if they don't look very similar, this hampers their growth since they learn to distrust intuitions which are actually correct.
        mindcrime 8y ago
        It might not prove that your solution is wrong, but it can help show that your solution is correct (if you trust the provided solution), and if you made a silly mistake in your solution then seeing someone else's solution might well help you spot it.
  - threwythrw 8y ago
    >Also, if you can’t prove a solution correct, then you haven’t solved it! This is the type of thinking I’m talking about. A beginner can think they “proved a solution correct” but have a subtle or even blantant error that isn’t obvious to them. Also, if reader wants to just skip to the solutions then that’s their fault. But don’t let such people rob the student that put serious effort into their work from seeing the solution.
- marktangotango 8y ago
  I also champion this method; I used solutions manuals as guides until I could internalize and reproduce the logic on my own. I was a particularly dense student though.
monktastic1 8y ago
Looks like no: "No solutions, sadly, but maybe that would be a good idea for a GitHub repo associated with the book…" https://jeremykun.com/2018/12/01/a-programmers-introduction-to-mathematics/#comment-69568 https://jeremykun.com/2018/12/01/a-programmers-introduction-...
- Kassius509 8y ago
  They have a repo. https://github.com/pim-book/programmers-introduction-to-mathematics https://github.com/pim-book/programmers-introduction-to-math...
pumanoir 8y ago
I would pay for the solutions as a book on its own. Solutions are essential for self learning, specially for tricky parts in mathematics i.e writing proofs, probability problems. I think the book “how to prove it” has good examples
k__ 8y ago
I read once, the key to mastery is perceptual exposure and deliberate practice. Don't know how the first part would work with Math.
- thatcat 8y ago
  Observing someones approaches at solutions and proofs would be perceptual exposure to mathematical analysis.
amelius 8y ago
> The most annoying things about math books is the lack of solutions. To me the most annoying thing about math books is hand-waving, lack of rigor, and unexplained notation. At least in programming, everything is formal and I can figure out the entire problem by looking at the source.
- kccqzy 8y ago
  I think you aren't buying very good math books then. I find the exact opposite: the thing about math books I have read is that they overemphasize rigor at the expense of intuition. Everything is painstakingly illustrated in such great detail that I sometimes see the trees and lose sight of the forest. I feel as if reading proofs and doing problem sets in math books is just manipulating symbols in well-known ways without really understanding intuitively why something must be true. For example my introduction to metric spaces started by defining the characteristics of a certain function d without explaining how this could be thought of as a generalization of distance. On the other hand, many programming stuff is ruefully hand-waving and lacks rigor. They might present important algorithms in pseudocode; even when they present in real code, the precise semantics of the real code is often underspecified and vaguely described in English. I mean take a language; how often do you see in the language specification the semantics of the language defined rigorously, using operational or denotational semantics? PL nitpicking aside, how many programmers think a piece of code must be correct because they pass a few test cases, without ever giving a proof? I'm of course not saying the lack of rigor in programming is bad. Perhaps 95% of the software we are building isn't mission-critical and relying on intuitions is fine; we ain't got no time to prove every piece of code we write. But my point is your observation really does not match mine.
  - andrepd 8y ago
    >the thing about math books I have read is that they overemphasize rigor at the expense of intuition I think these are not contradictory notions! Bad maths books lack rigour. Many books are like you say: rigorous but difficult to make sense of. But truly great books both explain the concepts in the simplest, most lucid and succinct way possible AND maintain the rigour necessary to do mathematics. I like this quote from Michael Spivak: "In addition to developing the students’ intuition [...], it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions." I couldn't agree more. Rigour is not a "masturbatory" end in itself to feel very smart, but it is not also an obstacle to understanding.
smadge 8y ago
A good math book has examples and proofs of theorems in the text that demonstrate what a solution should look like. In a sense, these ARE worked solutions to some problems. If you ever get stuck on an exercise, it helps to go back and look at those. Nothing beats having an expert to look at your solutions and provide feedback, though.
wilsonfiifi 8y ago
There seems to be a github repo [0]. It mentions code solutions to examples. [0] https://github.com/pim-book/programmers-introduction-to-mathematics

Koshkin 8y ago

Agree. Actually, studying a good solution even if you have one of your own is one of the best ways to learn mathematical tricks of the trade, so to speak - just as it's a great way to learn coding: one learns from the master (as one should) and not just "from the book."

chii 8y ago
being told a solution can sometimes lead to "rote" learning - where you learn a particular way of solving the problem, rather than applying creative thinking. Also, if you can't prove a solution correct, then you haven't solved it!
- ptd 8y ago
  Is this a feature or a bug? If it takes you two weeks to apply creative solutions and it take me one week to apply a “rote” solution, what is the benefit?
  - gbear605 8y ago
    The idea is that it might take you longer to learn, but when you are applying it in the real world and hit real world problems that are messy, you’ll be a lot faster
    - ptd 8y ago
      That’s the idea. In practice does it actually work out like that?
  - username90 8y ago
    The main reason to study mathematics is to build and fix your intuition, hence studying rote solutions is a waste of time. It might help you pass the class but it wont help you much at all in other parts of life. For example, at work nobody will care if you have rote memorized a solution or not since they will have already done the math, you will just apply formulas others have came up with. In order to do anything important with the math (not just solving school problems) you need to have intuition for it.
    - threwythrw 8y ago
      I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct. True beginners may think they have solid intuition and a rigorous proof, but without outside validation, may have a blantant or subtle error they cannot see. The point is not to study rote solutions, but to check correctness. Edit: To your reply below, I’m talking about someone that is self-studying and has no access to a teacher. The suggestion the beginner (without a teacher) should “know” whether or not their solutions are correct is something I disagree with. I do agree with there are multiple ways to prove something and such a beginner may think their proof is incorrect based on a provided solution, when it may be correct, just different. This is why an instructor is valuable.
      - username90 8y ago
        > I’d argue that a true beginner shouldn’t trust their intuition unless they have the rigor to prove it is correct. Yes, which is why you want a teacher until you reach that stage. > The point is not to study rote solutions, but to check correctness. Looking at others solutions can in no way prove that your solution is incorrect so I am not sure how those would help you. However having access to others solutions often makes students doubt their own solutions if they don't look very similar, this hampers their growth since they learn to distrust intuitions which are actually correct.
        mindcrime 8y ago
        It might not prove that your solution is wrong, but it can help show that your solution is correct (if you trust the provided solution), and if you made a silly mistake in your solution then seeing someone else's solution might well help you spot it.
- threwythrw 8y ago
  >Also, if you can’t prove a solution correct, then you haven’t solved it! This is the type of thinking I’m talking about. A beginner can think they “proved a solution correct” but have a subtle or even blantant error that isn’t obvious to them. Also, if reader wants to just skip to the solutions then that’s their fault. But don’t let such people rob the student that put serious effort into their work from seeing the solution.
marktangotango 8y ago
I also champion this method; I used solutions manuals as guides until I could internalize and reproduce the logic on my own. I was a particularly dense student though.

monktastic1 8y ago

Looks like no: "No solutions, sadly, but maybe that would be a good idea for a GitHub repo associated with the book…" https://jeremykun.com/2018/12/01/a-programmers-introduction-to-mathematics/#comment-69568 https://jeremykun.com/2018/12/01/a-programmers-introduction-...

Kassius509 8y ago
They have a repo. https://github.com/pim-book/programmers-introduction-to-mathematics https://github.com/pim-book/programmers-introduction-to-math...

pumanoir 8y ago

I would pay for the solutions as a book on its own. Solutions are essential for self learning, specially for tricky parts in mathematics i.e writing proofs, probability problems. I think the book “how to prove it” has good examples

k__ 8y ago

I read once, the key to mastery is perceptual exposure and deliberate practice. Don't know how the first part would work with Math.

thatcat 8y ago
Observing someones approaches at solutions and proofs would be perceptual exposure to mathematical analysis.

amelius 8y ago

> The most annoying things about math books is the lack of solutions. To me the most annoying thing about math books is hand-waving, lack of rigor, and unexplained notation. At least in programming, everything is formal and I can figure out the entire problem by looking at the source.

kccqzy 8y ago
I think you aren't buying very good math books then. I find the exact opposite: the thing about math books I have read is that they overemphasize rigor at the expense of intuition. Everything is painstakingly illustrated in such great detail that I sometimes see the trees and lose sight of the forest. I feel as if reading proofs and doing problem sets in math books is just manipulating symbols in well-known ways without really understanding intuitively why something must be true. For example my introduction to metric spaces started by defining the characteristics of a certain function d without explaining how this could be thought of as a generalization of distance. On the other hand, many programming stuff is ruefully hand-waving and lacks rigor. They might present important algorithms in pseudocode; even when they present in real code, the precise semantics of the real code is often underspecified and vaguely described in English. I mean take a language; how often do you see in the language specification the semantics of the language defined rigorously, using operational or denotational semantics? PL nitpicking aside, how many programmers think a piece of code must be correct because they pass a few test cases, without ever giving a proof? I'm of course not saying the lack of rigor in programming is bad. Perhaps 95% of the software we are building isn't mission-critical and relying on intuitions is fine; we ain't got no time to prove every piece of code we write. But my point is your observation really does not match mine.
- andrepd 8y ago
  >the thing about math books I have read is that they overemphasize rigor at the expense of intuition I think these are not contradictory notions! Bad maths books lack rigour. Many books are like you say: rigorous but difficult to make sense of. But truly great books both explain the concepts in the simplest, most lucid and succinct way possible AND maintain the rigour necessary to do mathematics. I like this quote from Michael Spivak: "In addition to developing the students’ intuition [...], it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions." I couldn't agree more. Rigour is not a "masturbatory" end in itself to feel very smart, but it is not also an obstacle to understanding.

smadge 8y ago

A good math book has examples and proofs of theorems in the text that demonstrate what a solution should look like. In a sense, these ARE worked solutions to some problems. If you ever get stuck on an exercise, it helps to go back and look at those. Nothing beats having an expert to look at your solutions and provide feedback, though.

wilsonfiifi 8y ago

There seems to be a github repo [0]. It mentions code solutions to examples. [0] https://github.com/pim-book/programmers-introduction-to-mathematics