FAQs: Preparing for College Math Study

tokenadult · June 9, 2007, 5:37pm

Back in the summer of 2003, I gathered up some Web links about how to study math. Any reader of this who has suggestions for additional links would surely be doing several readers of this thread a favor by sharing them, or by commenting on the links I post here.

[How</a> to Succeed in Math](<a href=“http://www.acad.sunytccc.edu/instruct/sbrown/math/succeed.htm]How”>http://www.acad.sunytccc.edu/instruct/sbrown/math/succeed.htm)

[Success</a> in Mathematics](<a href=“http://euler.slu.edu/Dept/SuccessinMath.html]Success”>http://euler.slu.edu/Dept/SuccessinMath.html)

[Understanding</a> Mathematics](<a href=“http://www.math.utah.edu/~alfeld/math.html]Understanding”>Understanding Mathematics)

[HOW</a> TO STUDY MATHEMATICS](<a href=“http://www.math.ohio-state.edu/counseling/how_to_study.html]HOW”>http://www.math.ohio-state.edu/counseling/how_to_study.html)

[Survival</a> Guide for Students Taking University Courses in Mathematics](<a href=“http://www.math.fau.edu/Niederhausen/HTML/SurvivalGuide.htm]Survival”>http://www.math.fau.edu/Niederhausen/HTML/SurvivalGuide.htm)

[Some</a> Help on Reading Mathematics and Creating Proofs](<a href=“http://math.ucsd.edu/~ebender/proofs.html]Some”>proofs)

[Education[/url</a>] (articles about undergraduate math study by Steven Zucker of Johns Hopkins U.)

[url=<a href="http://www.math.ohiou.edu/~mjm/goodproblems/goodstudent.html]Student’s">http://www.math.ohiou.edu/~mjm/goodproblems/goodstudent.html]Student’s</a> Guide to Good Problems<a href=“a%20great%20guide%20to%20mathematical%20writing”>/url</a>

[url=<a href=“http://www.maths.cam.ac.uk/undergrad/inductionday/studyskills/]STUDY”>http://www.maths.cam.ac.uk/undergrad/inductionday/studyskills/]STUDY</a> SKILLS IN MATHEMATICS<a href=“Cambridge%20University”>/url</a>

[url=<a href=“http://www.maths.ox.ac.uk/current-students/undergraduates/study-guide/]Study”>http://www.maths.ox.ac.uk/current-students/undergraduates/study-guide/]Study</a> Guide<a href=“Oxford%20University”>/url</a>

[url=<a href=“http://www.cargalmathbooks.com/]Books”>http://www.cargalmathbooks.com/]Books</a> in the Mathematical Sciences<a href=“James%20M.%20Cargal”>/url</a> more than just a book list, a guide full of opinions on how to learn different levels of mathematics

[url=<a href=“http://www.math.cornell.edu/~hubbard/readingmath.pdf]Reading”>http://www.math.cornell.edu/~hubbard/readingmath.pdf]Reading</a> Mathematics<a href=“Professor%20Hubbard%20at%20Cornell”>/url</a>

[url=<a href=“http://server1.fandm.edu/departments/Mathematics/writing_in_math/guide.html]Guide”>http://server1.fandm.edu/departments/Mathematics/writing_in_math/guide.html]Guide</a> to Writing in Mathematics Classes<a href=“Franklin%20and%20Marshall%20College”>/url</a>

[url=<a href=“http://www.esotericka.org/math/guide.html]Guide”>Guide to being a successful math student – Esotericka.org]Guide</a> to being a successful math student](<a href=“http://www.math.jhu.edu/~sz/Education/]Education[/url”>http://www.math.jhu.edu/~sz/Education/)

[Survival</a> Guide to Calculus<a href=“UC%20Berkeley”>/url</a>

[url=<a href=“Home | Academic Skills Center”>Home | Academic Skills Center]Learning</a> Strategies: Maximizing Your Academic Experience<a href=“Dartmouth%20College%20Academic%20Skills%20Center”>/url</a>

[url=<a href=“http://www.wadsworth.com/colsuccess_d/special_features/weblinks.html]Student”>http://www.wadsworth.com/colsuccess_d/special_features/weblinks.html]Student</a> Web Links<a href=“Wadsworth%20Publishing,%20links%20to%20many%20sites%20about%20study%20tips%20for%20all%20subjects”>/url</a>

Here are some famous pages on how to avoid errors in mathematics study:

[url=<a href=“http://www.math.vanderbilt.edu/~schectex/commerrs/]THE”>Common Errors in College Math]THE</a> MOST COMMON ERRORS IN UNDERGRADUATE MATHEMATICS](<a href=“http://math.berkeley.edu/~vojta/survival.html]Survival”>Survival Guide to Calculus)

[url=<a href=“Steve Maurer '67 (1946-2021) :: Swarthmore College”>Steve Maurer '67 (1946-2021) :: Swarthmore College]Common</a> Errors in Writing Mathematics<a href=“.PDF%20file”>/url</a>

Hope this helps!

paying3tuitions · June 9, 2007, 7:56pm

I just want to thank you for publishing this list.

May I ask, if you had to put an asterix next to one or two articles for students who had a terrible time with math in h.s. but somehow got into college anyway and will have to take the usual distribution requirement, which article(s) might you highlight?
I’m talking not about future math students, but those with mathphobia, fear and trembling etc.

tokenadult · June 9, 2007, 8:13pm

The first few best fit the situation of a student who has to take math in college but may not aspire to be a math major. The first link is not working just now as I try it, but the next three are.

Best wishes to the students you are cheering on.

paying3tuitions · June 9, 2007, 8:20pm

muchos gracias

purplexed · June 9, 2007, 8:58pm

Another thanks very much.

Printed “Survival Guide to Calculus,” for the person in my house who will likely face Calc. BC again in college. Perhaps the lessons from how NOT to study BC Calc. in high school will stick with her.

Some of those lessons:
Don’t ignore the book.
Don’t underestimate the time a class requires.
Don’t procrastinate.

And schedule classes, social life and work with this in mind: “How much should I study? …In one study, successful students put in about 14-15 hours per week outside of class to get an A…keep up with the class. Cramming doesn’t work.”

Seems like even the students at Georgia Tech hit the wall with BC Calc…must be a bit like orgo.

And maybe some of these links will help me if I try for the just the basic math for the GRE…

siserune · June 10, 2007, 7:51am

Hitting the wall isn’t from the calculus itself. According to a famous saying, “nobody fails calculus, they fail algebra and geometry while taking calculus”.

jmmom · June 10, 2007, 9:55am

Is there a corollary to paying3’s question - ie, are some of these geared toward the student going fairly far in math (while not a math major)? Say, a student who has great aptitude, likes the subject, but occasionally comes upon a course or teacher which is more difficult than usual?

oaklandmom · June 10, 2007, 10:03am

Here’s a link that was passed on to me by jbusc <a href=“http://web.mit.edu/jrickert/www/mathadvice.html[/url]”>http://web.mit.edu/jrickert/www/mathadvice.html</a> on how to write mathematical research papers.

tokenadult · June 10, 2007, 10:49am

Thanks, Oaklandmom, for the additional link. I’ve just had the pleasure of making the online acquaintance of the father of the author of that article, in a Mathematical Association of America special interest group on teaching advanced high school students.

To answer the question upthread, to some degree I tried to order the list so that the links for beginning math learners, and learners who might not go on to advanced math study, appear first. Some links for more advanced math learners (that is, learners of more advanced mathematical topics) come later in the list, although the ordering is not perfect and is debatable in any case. Some of the links are very specialized and some very general.

It would be delightful to see more links of this kind. Math courses in college often act as a “filter” in limiting students’ choices of further courses in some majors.

oaklandmom · June 10, 2007, 1:57pm

Thanks for starting this thread. I’ve actually been doing a little research to help my son figure out how write a mathematical research paper. In addition he solved a previously unsolved math problem(just a minor problem) and its been suggested he write it up for a math journal and he’s had no idea how to even begin that kind of writing, so we both appreciate any other links to articles that can help him think about how to write math papers.

tokenadult · June 10, 2007, 2:10pm

Oh, I should tell you about this link:

<a href=“http://www.artofproblemsolving.com/Resources/AoPS_R_A_HowWrite.php[/url]”>http://www.artofproblemsolving.com/Resources/AoPS_R_A_HowWrite.php</a>

It’s more geared to writing solutions to math competition problems, but some of the principles are general.

tokenadult · June 10, 2007, 2:40pm

Here’s Knuth et al. on mathematical writing:

<a href=“(La)TeX Navigator”>(La)TeX Navigator;

tokenadult · June 10, 2007, 6:27pm

I found a few new links, and updated a few links that were hosted on new university servers since I last updated the FAQ list.

[Preparing</a> for the California High School Exit Examination (CAHSEE): A Mathematics Study Guide](<a href=“http://www.cde.ca.gov/ta/tg/hs/mathguide.asp]Preparing”>http://www.cde.ca.gov/ta/tg/hs/mathguide.asp)

[How</a> to Succeed in Math](<a href=“http://www.sunytccc.edu/instruct/sbrown/math/succeed.htm]How”>http://www.sunytccc.edu/instruct/sbrown/math/succeed.htm)

[Success</a> in Mathematics](<a href=“http://euler.slu.edu/Dept/SuccessinMath.html]Success”>http://euler.slu.edu/Dept/SuccessinMath.html)

[College</a> Algebra<a href=“includes%20Tutorial%201” title=“How to Succeed in a Math Class”>/url</a>

[url=<a href=“http://www.math.clemson.edu/~mjs/courses/misc/study.pdf]How”>http://www.math.clemson.edu/~mjs/courses/misc/study.pdf]How</a> to Survive Your College Math Class (and Take Home Something of Value)<a href=“.PDF%20file”>/url</a>

[url=<a href=“http://www.iwu.edu/~lstout/HowToStudy.html]How”>http://www.iwu.edu/~lstout/HowToStudy.html]How</a> to Study Mathematics<a href=“Illinois%20Wesleyan”>/url</a>

[url=<a href=“http://www.math.utah.edu/~alfeld/math.html]Understanding”>Understanding Mathematics]Understanding</a> Mathematics](<a href=“http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/]College”>Virtual Math Lab - College Algebra)

[How</a> to Study Mathematics<a href=“The%20Ohio%20State%20University”>/url</a>

[url=<a href=“http://www.math.fau.edu/Niederhausen/HTML/SurvivalGuide.htm]Survival”>http://www.math.fau.edu/Niederhausen/HTML/SurvivalGuide.htm]Survival</a> Guide for Students Taking University Courses in Mathematics](<a href=“http://www.math.ohio-state.edu/students/how_to_study.html]How”>http://www.math.ohio-state.edu/students/how_to_study.html)

[Some</a> Help on Reading Mathematics and Creating Proofs](<a href=“http://math.ucsd.edu/~ebender/proofs.html]Some”>proofs)

[Education[/url</a>] (articles about undergraduate math study by Steven Zucker of Johns Hopkins U.)

[url=<a href="http://www.math.ohiou.edu/~mjm/goodproblems/goodstudent.html]Student’s">http://www.math.ohiou.edu/~mjm/goodproblems/goodstudent.html]Student’s</a> Guide to Good Problems<a href=“a%20great%20guide%20to%20mathematical%20writing”>/url</a>

[url=<a href=“http://www.maths.cam.ac.uk/undergrad/inductionday/studyskills/”>http://www.maths.cam.ac.uk/undergrad/inductionday/studyskills/</a>] Study Skills in Mathematics<a href=“Cambridge%20University”>/url</a>

[url=<a href=“http://www.maths.ox.ac.uk/current-students/undergraduates/study-guide/]Study”>http://www.maths.ox.ac.uk/current-students/undergraduates/study-guide/]Study</a> Guide<a href=“Oxford%20University”>/url</a>

[url=<a href=“http://www.math.purdue.edu/academic/undergrad/credit/undergrad]Credit”>Credit Exams for Undergraduates - Department of Mathematics - Purdue University]Credit</a> Exams for Undergraduates](<a href=“http://www.math.jhu.edu/~sz/Education/]Education[/url”>http://www.math.jhu.edu/~sz/Education/) lots of study guides and practice exams for undergraduate math courses

[Reading</a> Mathematics<a href=“Professor%20Hubbard%20at%20Cornell”>/url</a>

[url=<a href=“http://www.cargalmathbooks.com/]Books”>http://www.cargalmathbooks.com/]Books</a> in the Mathematical Sciences<a href=“James%20M.%20Cargal”>/url</a> more than just a book list, a guide full of opinions on how to learn different levels of mathematics

[url=<a href=“http://www.ocf.berkeley.edu/~abhishek/chicmath.htm]Chicago”>Chicago undergraduate mathematics bibliography]Chicago</a> undergraduate mathematics bibliography](<a href=“http://www.math.cornell.edu/~hubbard/readingmath.pdf]Reading”>http://www.math.cornell.edu/~hubbard/readingmath.pdf) a book list and an introduction to studying math at the U of Chicago

[Guide</a> to Writing in Mathematics Classes<a href=“Franklin%20and%20Marshall%20College”>/url</a>

[url=<a href=“http://www.esotericka.org/math/guide.html]Guide”>Guide to being a successful math student – Esotericka.org]Guide</a> to being a successful math student](<a href=“http://server1.fandm.edu/departments/Mathematics/writing_in_math/guide.html]Guide”>http://server1.fandm.edu/departments/Mathematics/writing_in_math/guide.html)

[Survival</a> Guide to Calculus<a href=“UC%20Berkeley”>/url</a>

[url=<a href=“http://web.mit.edu/jrickert/www/mathadvice.html]Writing”>http://web.mit.edu/jrickert/www/mathadvice.html]Writing</a> a Research Paper in Mathematics<a href=“Ashley%20Reiter”>/url</a>

[url=<a href=“(La)TeX Navigator”>(La)TeX Navigator]Mathematical</a> Writing<a href=“Donald%20E.%20Knuth,%20Tracy%20Larrabee,%20and%20Paul%20M.%20Roberts”>/url</a>

[url=<a href=“Home | Academic Skills Center”>Home | Academic Skills Center]Learning</a> Strategies: Maximizing Your Academic Experience<a href=“Dartmouth%20College%20Academic%20Skills%20Center”>/url</a>

[url=<a href=“http://www.wadsworth.com/colsuccess_d/special_features/weblinks.html]Student”>http://www.wadsworth.com/colsuccess_d/special_features/weblinks.html]Student</a> Web Links<a href=“Wadsworth%20Publishing,%20links%20to%20many%20sites%20about%20study%20tips%20for%20all%20subjects”>/url</a>

[url=<a href=“http://math.arizona.edu/ugprogram/mcenter/gradprep.html]How”>Preparing For Eventual Entry into a Graduate Program in the Mathematical Sciences - Department of Mathematics]How</a> to prepare for a graduate program in the mathematical sciences<a href=“U.%20of%20Arizona”>/url</a>

Here are some famous pages on how to avoid errors in mathematics study:

[url=<a href=“http://www.math.vanderbilt.edu/~schectex/commerrs/]THE”>Common Errors in College Math]THE</a> MOST COMMON ERRORS IN UNDERGRADUATE MATHEMATICS](<a href=“http://math.berkeley.edu/~vojta/survival.html]Survival”>Survival Guide to Calculus)

[url=<a href=“Steve Maurer '67 (1946-2021) :: Swarthmore College”>Steve Maurer '67 (1946-2021) :: Swarthmore College]Common</a> Errors in Writing Mathematics<a href=“.PDF%20file”>/url</a>

Enjoy. I’d be glad to hear of other useful links. In general, the ordering principle is from links about most high-school-like levels of math to most grad-school-like, and a few of the links just before the section about mistakes are links to general study guide sites, so that a young math student can do well in subjects other than math. So beginners at college math should start at the beginning of the list.

mathmom · June 10, 2007, 9:38pm

The mathforum.org and in particular the Ask Dr. Math portion is great. I used it most often when asked questions by Mathson I no longer remembered answers to - but often then got beguiled by exploring. I remember a lot of fun things about Magic Squares, lots of math for all levels.

tokenadult · June 10, 2007, 10:45pm

Yes, mathmom, [Math</a> Forum](<a href=“Classroom Resources - National Council of Teachers of Mathematics”>http://mathforum.org/) is an interesting resource. I had a different kind of resource in mind when I compiled my FAQ, but thanks for mentioning Math Forum in this thread.

johnshade · June 11, 2007, 4:30pm

Good stuff. I would also strongly recommend one book, G. Polya’s How to Solve It, which I only recently read and wish to goodness I had read before embarking on my undergrad math major (actually, it’s a great book for a high school student with a math knack who wants to get to the next level).

PS - I had Steve Maurer, author of the last link, as a teacher in high school. He was a great teacher and a great guy, and I’m pleased to see he is now chair of the Swarthmore math department.

tokenadult · July 10, 2007, 10:35am

Bumping by replying to the last post. My son had Professor Maurer as one of several teachers in a summer program two years ago. Maurer is a good teacher.

Oiram · August 20, 2007, 8:27pm

Bring up this post for college students of the fall 2007.

tokenadult · August 21, 2007, 12:39am

Thanks for the bump. I hope this is helpful to students starting college this year.

NYMomof2 · August 21, 2007, 10:19am

Thank you very much for the thread, tokenadult. And thanks to everyone else who contributed. This will be very useful.

FAQs: Preparing for College Math Study

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