Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Topology - prerequisites

  1. Oct 28, 2008 #1
    Hello,
    I'm wondering, is it possible to study topology without having taken a course in multivariable calculus? I'm very eager to learn and my college don't offer too many math courses this spring (I'm moving to a bigger next fall though), so I'm thinking if I should take topology. I can basically put in unlimited time of study to grasp it.

    Best regards,
    Magnus
     
  2. jcsd
  3. Oct 28, 2008 #2
    Learning topology requires some knowledge of basic set theory, but little more than that.
     
  4. Oct 28, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I would say that the most important "prerequisite" is mathematical maturity which is, basically, the abitility to understand and use specific definitions and to write good proofs.
     
    Last edited: Oct 31, 2008
  5. Oct 28, 2008 #4

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    And if you don't have that mathematical maturity, I can't think of a better way to obtain it than to study topology because most "theorems" in point set topology follow trivially from the definitions...
     
  6. Oct 28, 2008 #5

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    try this topology book for high school students:

    First Concepts of Topology; The Geometry of Mappings of Segments, Curves, Circles, and Disks
    Chinn, W. G.; Steenrod, N. E.



    [30 Day Returns Policy]
    Bookseller:
    Clausen Books, RMABA
    (Colorado Springs, CO, U.S.A.)
    Bookseller Rating: Book Price:
    US$ 10.00
     
  7. Oct 29, 2008 #6
    d_leet
    I know basic set theory, so that probably won't be a problem.

    Hallsofivy, quasar987

    I wouldn't say that I'm mathematically mature in any manner, but I have a will to learn. I've been getting straight As all the way in math, but that probably doesn't show anything. But one day, I hope to have accumulated enough experience to be able to refer to myself as mathematically mature. Do you both think that topology would be a good task to undertake to gain a bit of this experience?

    Mathwonk
    Thanks, I just bought it. I have to say that you and everyone else (none mentioned, none forgotten) really inspire me. To every homework helper and everyone that gives tips, thanks. Off topic, but I just want it off my chest.
     
  8. Oct 29, 2008 #7

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    thank you. good luck. you are a wise man.
     
  9. Oct 30, 2008 #8
    I don't know if I could call myself a man at age 18, though.

    Anyhow, the course book is "Principles of mathematical analysis" aka "Baby Rudin". How is it? Are there any special prerequisites for it except the ones mentioned above?
     
  10. Oct 30, 2008 #9

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    this book is an excellent source of correct information, but a poor source of explanation of that material for most students, being overly terse. i.e. the author is a good analyst but a poor pedagogue.
     
  11. Oct 31, 2008 #10
    Is there any book that I could use as a supplement to it?
     
  12. Oct 31, 2008 #11

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    as a young instructor i found the books of george simmons much more readable.

    Introduction to Topology and Modern Analysis International Series in Pure and Applied Mathematics
    Simmons, George F



    [30 Day Returns Policy]
    Bookseller:
    Cellar Stories Bookstore
    (Providence, RI, U.S.A.)
    Bookseller Rating: Book Price:
    US$ 10.00
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Topology - prerequisites
  1. DNA Topology (Replies: 2)

  2. Problem in topology (Replies: 15)

  3. Differential Topology (Replies: 0)

Loading...