Sources of Math Problems to Maintain One's “Chops”












4












$begingroup$


I got partway through a graduate degree in math and I'm now doing something "completely different," but it bothers me that my skills are fading away. I don't have a lot of time, but I would like to devote 15 - 30 minutes a day to working on a problem, or some problems.



I'm curious where you'd look for problems if you were in a similar situation...



Here are some ideas to get started:




  • Martin Gardner books

  • Project Euler (but do the problems without computers)

  • Measurement by Paul Lockhart


I wonder about textbooks. It's hard to push oneself through textbooks outside of a class, peers, deadlines. Maybe there are some which would be friendlier than others in this regard...?



EDIT:



The 15 - 30 minutes thing is a bit arbitrary. I'm just saying I can't count on having lots of time to spend. I started reading Munkres's Topology again, and Gleason's analysis book, intending to take my time, do most of the exercises, etc..



I suppose there aren't any specific skills I'm most interested in maintaining, but I was just looking to see if you had some ideas for ways to keep my head in the game.






soft-question







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    What skills are you concerned about sharpening?
    $endgroup$
    – Don Thousand
    Dec 18 '18 at 21:13






  • 4




    $begingroup$
    I think Marvin is actually called Martin! (I can't make a 1-character edit to correct it, but as the post author you can.)
    $endgroup$
    – timtfj
    Dec 18 '18 at 21:32






  • 1




    $begingroup$
    I do not make a habit of Project Euler problems, but I would not recommend trying to really answer them without a computer. The problems are designed with programming in mind; they are meant to be such that even getting a computer to do it requires ingenuity. So they are presumably designed to require huge computations; definitely not a 15-30 minute thing! That said, if you wanted to then you could try to think about what the best algorithm would be; but then imo you might as well implement it to make sure it works the way you want it to.
    $endgroup$
    – Will R
    Dec 18 '18 at 22:16










  • $begingroup$
    So similarly I studied math and now I am doing something that does not at all use my studies, though I did get the PhD. I use this site. It seems that when school is out, good problems are few and far between, but during the fall and spring semesters there's lots to do. I also still do my research as a hobby, with no plans of publishing unless I hit the jackpot.
    $endgroup$
    – Matt Samuel
    Dec 19 '18 at 2:38










  • $begingroup$
    Fixed that spelling blip. Thanks timtfj.
    $endgroup$
    – user3050028
    Dec 20 '18 at 19:45
















4












$begingroup$


I got partway through a graduate degree in math and I'm now doing something "completely different," but it bothers me that my skills are fading away. I don't have a lot of time, but I would like to devote 15 - 30 minutes a day to working on a problem, or some problems.



I'm curious where you'd look for problems if you were in a similar situation...



Here are some ideas to get started:




  • Martin Gardner books

  • Project Euler (but do the problems without computers)

  • Measurement by Paul Lockhart


I wonder about textbooks. It's hard to push oneself through textbooks outside of a class, peers, deadlines. Maybe there are some which would be friendlier than others in this regard...?



EDIT:



The 15 - 30 minutes thing is a bit arbitrary. I'm just saying I can't count on having lots of time to spend. I started reading Munkres's Topology again, and Gleason's analysis book, intending to take my time, do most of the exercises, etc..



I suppose there aren't any specific skills I'm most interested in maintaining, but I was just looking to see if you had some ideas for ways to keep my head in the game.






soft-question







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    What skills are you concerned about sharpening?
    $endgroup$
    – Don Thousand
    Dec 18 '18 at 21:13






  • 4




    $begingroup$
    I think Marvin is actually called Martin! (I can't make a 1-character edit to correct it, but as the post author you can.)
    $endgroup$
    – timtfj
    Dec 18 '18 at 21:32






  • 1




    $begingroup$
    I do not make a habit of Project Euler problems, but I would not recommend trying to really answer them without a computer. The problems are designed with programming in mind; they are meant to be such that even getting a computer to do it requires ingenuity. So they are presumably designed to require huge computations; definitely not a 15-30 minute thing! That said, if you wanted to then you could try to think about what the best algorithm would be; but then imo you might as well implement it to make sure it works the way you want it to.
    $endgroup$
    – Will R
    Dec 18 '18 at 22:16










  • $begingroup$
    So similarly I studied math and now I am doing something that does not at all use my studies, though I did get the PhD. I use this site. It seems that when school is out, good problems are few and far between, but during the fall and spring semesters there's lots to do. I also still do my research as a hobby, with no plans of publishing unless I hit the jackpot.
    $endgroup$
    – Matt Samuel
    Dec 19 '18 at 2:38










  • $begingroup$
    Fixed that spelling blip. Thanks timtfj.
    $endgroup$
    – user3050028
    Dec 20 '18 at 19:45














4












4








4


1



$begingroup$


I got partway through a graduate degree in math and I'm now doing something "completely different," but it bothers me that my skills are fading away. I don't have a lot of time, but I would like to devote 15 - 30 minutes a day to working on a problem, or some problems.



I'm curious where you'd look for problems if you were in a similar situation...



Here are some ideas to get started:




  • Martin Gardner books

  • Project Euler (but do the problems without computers)

  • Measurement by Paul Lockhart


I wonder about textbooks. It's hard to push oneself through textbooks outside of a class, peers, deadlines. Maybe there are some which would be friendlier than others in this regard...?



EDIT:



The 15 - 30 minutes thing is a bit arbitrary. I'm just saying I can't count on having lots of time to spend. I started reading Munkres's Topology again, and Gleason's analysis book, intending to take my time, do most of the exercises, etc..



I suppose there aren't any specific skills I'm most interested in maintaining, but I was just looking to see if you had some ideas for ways to keep my head in the game.






soft-question







share|cite|improve this question











$endgroup$




I got partway through a graduate degree in math and I'm now doing something "completely different," but it bothers me that my skills are fading away. I don't have a lot of time, but I would like to devote 15 - 30 minutes a day to working on a problem, or some problems.



I'm curious where you'd look for problems if you were in a similar situation...



Here are some ideas to get started:




  • Martin Gardner books

  • Project Euler (but do the problems without computers)

  • Measurement by Paul Lockhart


I wonder about textbooks. It's hard to push oneself through textbooks outside of a class, peers, deadlines. Maybe there are some which would be friendlier than others in this regard...?



EDIT:



The 15 - 30 minutes thing is a bit arbitrary. I'm just saying I can't count on having lots of time to spend. I started reading Munkres's Topology again, and Gleason's analysis book, intending to take my time, do most of the exercises, etc..



I suppose there aren't any specific skills I'm most interested in maintaining, but I was just looking to see if you had some ideas for ways to keep my head in the game.






soft-question




soft-question






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 20 '18 at 19:53







user3050028

















asked Dec 18 '18 at 21:04









user3050028user3050028

242




242








  • 1




    $begingroup$
    What skills are you concerned about sharpening?
    $endgroup$
    – Don Thousand
    Dec 18 '18 at 21:13






  • 4




    $begingroup$
    I think Marvin is actually called Martin! (I can't make a 1-character edit to correct it, but as the post author you can.)
    $endgroup$
    – timtfj
    Dec 18 '18 at 21:32






  • 1




    $begingroup$
    I do not make a habit of Project Euler problems, but I would not recommend trying to really answer them without a computer. The problems are designed with programming in mind; they are meant to be such that even getting a computer to do it requires ingenuity. So they are presumably designed to require huge computations; definitely not a 15-30 minute thing! That said, if you wanted to then you could try to think about what the best algorithm would be; but then imo you might as well implement it to make sure it works the way you want it to.
    $endgroup$
    – Will R
    Dec 18 '18 at 22:16










  • $begingroup$
    So similarly I studied math and now I am doing something that does not at all use my studies, though I did get the PhD. I use this site. It seems that when school is out, good problems are few and far between, but during the fall and spring semesters there's lots to do. I also still do my research as a hobby, with no plans of publishing unless I hit the jackpot.
    $endgroup$
    – Matt Samuel
    Dec 19 '18 at 2:38










  • $begingroup$
    Fixed that spelling blip. Thanks timtfj.
    $endgroup$
    – user3050028
    Dec 20 '18 at 19:45














  • 1




    $begingroup$
    What skills are you concerned about sharpening?
    $endgroup$
    – Don Thousand
    Dec 18 '18 at 21:13






  • 4




    $begingroup$
    I think Marvin is actually called Martin! (I can't make a 1-character edit to correct it, but as the post author you can.)
    $endgroup$
    – timtfj
    Dec 18 '18 at 21:32






  • 1




    $begingroup$
    I do not make a habit of Project Euler problems, but I would not recommend trying to really answer them without a computer. The problems are designed with programming in mind; they are meant to be such that even getting a computer to do it requires ingenuity. So they are presumably designed to require huge computations; definitely not a 15-30 minute thing! That said, if you wanted to then you could try to think about what the best algorithm would be; but then imo you might as well implement it to make sure it works the way you want it to.
    $endgroup$
    – Will R
    Dec 18 '18 at 22:16










  • $begingroup$
    So similarly I studied math and now I am doing something that does not at all use my studies, though I did get the PhD. I use this site. It seems that when school is out, good problems are few and far between, but during the fall and spring semesters there's lots to do. I also still do my research as a hobby, with no plans of publishing unless I hit the jackpot.
    $endgroup$
    – Matt Samuel
    Dec 19 '18 at 2:38










  • $begingroup$
    Fixed that spelling blip. Thanks timtfj.
    $endgroup$
    – user3050028
    Dec 20 '18 at 19:45








1




1




$begingroup$
What skills are you concerned about sharpening?
$endgroup$
– Don Thousand
Dec 18 '18 at 21:13




$begingroup$
What skills are you concerned about sharpening?
$endgroup$
– Don Thousand
Dec 18 '18 at 21:13




4




4




$begingroup$
I think Marvin is actually called Martin! (I can't make a 1-character edit to correct it, but as the post author you can.)
$endgroup$
– timtfj
Dec 18 '18 at 21:32




$begingroup$
I think Marvin is actually called Martin! (I can't make a 1-character edit to correct it, but as the post author you can.)
$endgroup$
– timtfj
Dec 18 '18 at 21:32




1




1




$begingroup$
I do not make a habit of Project Euler problems, but I would not recommend trying to really answer them without a computer. The problems are designed with programming in mind; they are meant to be such that even getting a computer to do it requires ingenuity. So they are presumably designed to require huge computations; definitely not a 15-30 minute thing! That said, if you wanted to then you could try to think about what the best algorithm would be; but then imo you might as well implement it to make sure it works the way you want it to.
$endgroup$
– Will R
Dec 18 '18 at 22:16




$begingroup$
I do not make a habit of Project Euler problems, but I would not recommend trying to really answer them without a computer. The problems are designed with programming in mind; they are meant to be such that even getting a computer to do it requires ingenuity. So they are presumably designed to require huge computations; definitely not a 15-30 minute thing! That said, if you wanted to then you could try to think about what the best algorithm would be; but then imo you might as well implement it to make sure it works the way you want it to.
$endgroup$
– Will R
Dec 18 '18 at 22:16












$begingroup$
So similarly I studied math and now I am doing something that does not at all use my studies, though I did get the PhD. I use this site. It seems that when school is out, good problems are few and far between, but during the fall and spring semesters there's lots to do. I also still do my research as a hobby, with no plans of publishing unless I hit the jackpot.
$endgroup$
– Matt Samuel
Dec 19 '18 at 2:38




$begingroup$
So similarly I studied math and now I am doing something that does not at all use my studies, though I did get the PhD. I use this site. It seems that when school is out, good problems are few and far between, but during the fall and spring semesters there's lots to do. I also still do my research as a hobby, with no plans of publishing unless I hit the jackpot.
$endgroup$
– Matt Samuel
Dec 19 '18 at 2:38












$begingroup$
Fixed that spelling blip. Thanks timtfj.
$endgroup$
– user3050028
Dec 20 '18 at 19:45




$begingroup$
Fixed that spelling blip. Thanks timtfj.
$endgroup$
– user3050028
Dec 20 '18 at 19:45










1 Answer
1






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$begingroup$

I find that training problems for mathematical competitions are a good exercise to keep your mind sharp. For example there are




  • Training problems for the Putnam competition


  • Questions from the ITYM


  • A list of problems considered to be standard by Arnol'd:
    Arnold's Trivium



An exercise-rich textbook is Atiyah's & McDonalds Commutative Algebra. Depending on your background their exercises might be challenging or the daily 10-15min exercise for you.



P.S.: I have been actively collecting problems involving a "trick" for a couple of years and am sure others have done so as well. Maybe you will find some of these by a google search?






share|cite|improve this answer









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    $begingroup$

    I find that training problems for mathematical competitions are a good exercise to keep your mind sharp. For example there are




    • Training problems for the Putnam competition


    • Questions from the ITYM


    • A list of problems considered to be standard by Arnol'd:
      Arnold's Trivium



    An exercise-rich textbook is Atiyah's & McDonalds Commutative Algebra. Depending on your background their exercises might be challenging or the daily 10-15min exercise for you.



    P.S.: I have been actively collecting problems involving a "trick" for a couple of years and am sure others have done so as well. Maybe you will find some of these by a google search?






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      I find that training problems for mathematical competitions are a good exercise to keep your mind sharp. For example there are




      • Training problems for the Putnam competition


      • Questions from the ITYM


      • A list of problems considered to be standard by Arnol'd:
        Arnold's Trivium



      An exercise-rich textbook is Atiyah's & McDonalds Commutative Algebra. Depending on your background their exercises might be challenging or the daily 10-15min exercise for you.



      P.S.: I have been actively collecting problems involving a "trick" for a couple of years and am sure others have done so as well. Maybe you will find some of these by a google search?






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        I find that training problems for mathematical competitions are a good exercise to keep your mind sharp. For example there are




        • Training problems for the Putnam competition


        • Questions from the ITYM


        • A list of problems considered to be standard by Arnol'd:
          Arnold's Trivium



        An exercise-rich textbook is Atiyah's & McDonalds Commutative Algebra. Depending on your background their exercises might be challenging or the daily 10-15min exercise for you.



        P.S.: I have been actively collecting problems involving a "trick" for a couple of years and am sure others have done so as well. Maybe you will find some of these by a google search?






        share|cite|improve this answer









        $endgroup$



        I find that training problems for mathematical competitions are a good exercise to keep your mind sharp. For example there are




        • Training problems for the Putnam competition


        • Questions from the ITYM


        • A list of problems considered to be standard by Arnol'd:
          Arnold's Trivium



        An exercise-rich textbook is Atiyah's & McDonalds Commutative Algebra. Depending on your background their exercises might be challenging or the daily 10-15min exercise for you.



        P.S.: I have been actively collecting problems involving a "trick" for a couple of years and am sure others have done so as well. Maybe you will find some of these by a google search?







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 18 '18 at 21:17









        Card_TrickCard_Trick

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