Answers.Body: <p>John Kemeny et all have published a set of books on Finite Mathematics that are classics. They have lots of exercises but no solutions in the books themselves. However, the solutions guide may be available for some of them online or <em>especially</em> at eBay with a suitable search. </p>
  
  <p>One of the classics is <a href="https://rads.stackoverflow.com/amzn/click/0133173216" rel="nofollow noreferrer">Finite Mathematics with Business Applications</a>. Don't let the title fool you. It is serious mathematics. </p>
  
  <p>Another, more common and possibly lighter weight book is <a href="https://rads.stackoverflow.com/amzn/click/0134838343" rel="nofollow noreferrer">Introduction to Finite Mathematics</a></p>
  
  <p>These books are both old and out of print, but readily available. I think the latter one is available as a PDF online (but without answers). </p>
  
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Answers.UserDisplayName: Buffy
Answers.Body: <p>Most of the maths in undergraduate CS is proof by structural induction (and we do at least in part deserve the reputation we have among mathematicians of not knowing that there are other proof techniques). That technique apart, the "non-CS" maths can be more than covered by chapters 2 and 4 of <a href="https://www.amazon.es/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025" rel="nofollow noreferrer">Concrete Mathematics</a>, Graham, Knuth, and Patashnik, ISBN: 0-201-55802-5. This book contains many exercises and solutions thereof, or hints in the case of unsolved problems. There are PDFs available online, but I'm not sure whether they're authorised so I won't link to any.</p>
  
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Answers.Text: The Amazon link at the US site is: https://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025/ and yes, Structural Induction is a big win.
Answers.UserDisplayName: Buffy
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Answers.Text: Other proof techniques like what?  :D  (But really?)
Answers.UserDisplayName: Wildcard
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Answers.Text: @Wildcard, [proof by intimidation, proof by eminent authority](http://mfleck.cs.illinois.edu/proof.html), etc. ;) More seriously, there are proofs by contradiction and by construction in CS, but proof by structural induction is the natural fit when so many proofs are precisely about structures which are defined recursively.
Answers.UserDisplayName: Peter Taylor
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Answers.UserDisplayName: Peter Taylor
Body: <p>A student studying Computer Science requires some knowledge of finite mathematics, including logic, probability, counting, etc. In the use-case at hand, a HS or University course in finite math is not an option as the student is self studying. </p>
  
  <p>What are good resources by which a student can learn the necessary material to support a CS degree? These could be books or online resources or perhaps other things not yet considered. </p>
  
  <p>However, one essential aspect is that the student needs access to materials by which the topics can be practiced, not just read about. Resources with lots of exercises at different levels with a way to obtain feedback (answer key or other) would be essential. </p>
  
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Comments.Text: The necessary material surely depends on the syllabus of the CS degree. I don't remember ever needing probability or combinatorics (which I assume is what you mean by "*counting*"). Could you be more specific about the requirements?
Comments.UserDisplayName: Peter Taylor
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Comments.Text: Courses in finite/discrete math often include at least elementary combinatorics and some probability. I'm surprised yours had no need of it at all.
Comments.UserDisplayName: Buffy
Tags: <resource-request><self-learning><finite-mathematics>
Title: What are good resources for self learning Finite Mathematics for a CS Student?
ThreadText: # What are good resources for self learning Finite Mathematics for a CS Student?
  
  (Asked by: username_0 on 2018-01-24)
  
  A student studying Computer Science requires some knowledge of finite mathematics, including logic, probability, counting, etc. In the use-case at hand, a HS or University course in finite math is not an option as the student is self studying.
  
  What are good resources by which a student can learn the necessary material to support a CS degree? These could be books or online resources or perhaps other things not yet considered.
  
  However, one essential aspect is that the student needs access to materials by which the topics can be practiced, not just read about. Resources with lots of exercises at different levels with a way to obtain feedback (answer key or other) would be essential.
  
  **Tags:** resource-request, self-learning, finite-mathematics
  
  > **Comments:**
  > **username_1**: The necessary material surely depends on the syllabus of the CS degree. I don't remember ever needing probability or combinatorics (which I assume is what you mean by "*counting*"). Could you be more specific about the requirements?  
  > **username_0**: Courses in finite/discrete math often include at least elementary combinatorics and some probability. I'm surprised yours had no need of it at all.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_0 on 2018-01-24. Score: 3
  
  John Kemeny et all have published a set of books on Finite Mathematics that are classics. They have lots of exercises but no solutions in the books themselves. However, the solutions guide may be available for some of them online or *especially* at eBay with a suitable search.
  
  One of the classics is [Finite Mathematics with Business Applications](https://rads.stackoverflow.com/amzn/click/0133173216). Don't let the title fool you. It is serious mathematics.
  
  Another, more common and possibly lighter weight book is [Introduction to Finite Mathematics](https://rads.stackoverflow.com/amzn/click/0134838343)
  
  These books are both old and out of print, but readily available. I think the latter one is available as a PDF online (but without answers).
  
  
  ---
  
  ### Answer by username_1 on 2018-01-29. Score: 3
  
  Most of the maths in undergraduate CS is proof by structural induction (and we do at least in part deserve the reputation we have among mathematicians of not knowing that there are other proof techniques). That technique apart, the "non-CS" maths can be more than covered by chapters 2 and 4 of [Concrete Mathematics](https://www.amazon.es/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025), Graham, Knuth, and Patashnik, ISBN: 0-201-55802-5. This book contains many exercises and solutions thereof, or hints in the case of unsolved problems. There are PDFs available online, but I'm not sure whether they're authorised so I won't link to any.
  
  > **Comments:**
  > **username_0**: The Amazon link at the US site is: https://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025/ and yes, Structural Induction is a big win.  
  > **username_2**: Other proof techniques like what?  :D  (But really?)  
  > **username_1**: @username_2, [proof by intimidation, proof by eminent authority](http://mfleck.cs.illinois.edu/proof.html), etc. ;) More seriously, there are proofs by contradiction and by construction in CS, but proof by structural induction is the natural fit when so many proofs are precisely about structures which are defined recursively.  
  
  ---
  
  