Mathematics Students discussion

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Topology > Potential topology study group

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message 1: by Chris (new)

Chris Aldrich (chrisaldrich) | 19 comments I'm cross-posting this comment (with very minor logical changes) from another thread in an effort to push along a broader conversation.

I tend to stay away from some of the biographical work on mathematics as it's usually fairly droll and the scholarship underpinning the majority of it is generally weak at best - presumably because there are sexier topics for writers and historians.

I've dabbled from time to time in topology and even algebraic topology and would be happy to join in a conversation on either. I'm a fan of Munkres' text which was mentioned by Ronald. Perhaps if anyone is aware of any online lecture series on topology (via youtube, NPTEL, or other?) we might use that in addition to a textbook to focus some effort. Perhaps using Google+ for online video conferencing?

In an effort to help push things along on this topic (rather than the slow pace the previous thread had been on - since July), I've added Munkres' text to the group's "currently reading" list and created a discussion folder for "Topology" in general. Perhaps we can use this as a stub to draw the attention of others and eventually settle on a specific book (or two) to get a group of 3-5 people moving in the same direction?

I haven't heard any upper-level math topics mentioned in any of the MOOC's lately (Coursera, EdX, Udacity, et al.), but if a free online class popped up, perhaps that might be a good way to push some broader discussion here. Is anyone aware of anything interesting coming up?

For those like Theresa, who are out of school - and depending on your location - you might find a local school/university that offers Extension/evening classes in an area of math you're interested in. As an example, in LA, I've been going to evening classes in upper level undergrad/graduate level math through UCLA extension for the past several years with a rotating group of 50+ colleagues. Check around in your neighborhood to see what is available. I've managed to do some reasonable work in differential geometry, abstract algebra, analysis, integer partitions, combinatorics, algebraic topology, Galois theory, and others as a result of this - these days I'll take almost anything they offer. I'm planning on taking a course in measure theory beginning in January if anyone is interested in following along on that subject via my notes and supplementary texts.

I look forward to everyone's thoughts/comments.


message 2: by Theresa (new)

Theresa Ramseyer | 25 comments I did pick up the following books from MSSU's library:

Three-Dimensional Geometry and Topology, Thurston, Vol. 1 (started reading it, looks like fun!)

Mathematical Tourist, Ivars Peterson. Not the Topology/games book I was looking for, but I couldn't find the latter quickly, and this also has other cool subjects.

The Knot Book, Adams

Algebraic Topology, Agoston

Mathematical Basis of the Arts. Joseph Schillinger.

Plus two women in mathematics books.

I'm having problems getting the Munkres' book.

Sorry for the delay in posting otherwise, I have to run.

Theresa


message 3: by Ronald (new)

Ronald Lett (slider142) | 15 comments Thurston's book is a lot of fun. I wouldn't mind going through that one myself, as I've mostly only found time to dip into it. The Knot Book I would also like to go through again.
Another, slightly more modern, perspective on algebraic topology can be found here: http://www.math.cornell.edu/~hatcher/... (I have the paperback for portability reasons).
What are the two women in mathematics books that you found ?


message 4: by Theresa (new)

Theresa Ramseyer | 25 comments Ronald, I found:

Women of mathematics : a biobibliographic sourcebook / edited by Louise S. Grinstein and Paul J. Campbell ; with a foreword by Alice Schafer.

and

Math equals : biographies of women mathematicians + related activities / Teri Perl.

I am returning the Perl book today, and the Algebraic Topology book. Keeping the Thurston book, the Knot Book (Adams) and changing my mind to keep Men in Mathematics.

I won't be back to MSSU's library for probably a couple of weeks. Depends on the weather, and how fast someone can find out what's going on with my brakes and fix them, etc.

I have a couple of other reading groups that are really busy this month (December). Plus of course concert, the Hobbit, the holidays and so forth - so I apologize for being slower than usual.

I would also like to get into the book the Mathematical Basis of the Arts, borrowed from MSSU.

I am very glad that this is not MSSU's library's inventory year, and I can check books out over the holiday break.

Theresa


message 5: by Theresa (new)

Theresa Ramseyer | 25 comments With my apologies for not being able to contribute, I'm leaving the group this morning. I have never been someone who likes to just up and bail without notice. Frankly, I don't have the time or the money to lead this discussion, and/or the ability to get the book. I won't for several months at minimum.

Again, I'm sorry that my intentions were bigger than my abilities!

Take care,
Theresa


message 6: by Theresa (new)

Theresa Ramseyer | 25 comments With my apologies for not being able to contribute, I'm leaving the group this morning. I have never been someone who likes to just up and bail without notice. Frankly, I don't have the time or the money to lead this discussion, and/or the ability to get the book. I won't for several months at minimum.

Again, I'm sorry that my intentions were bigger than my abilities!

Take care,
Theresa


message 7: by Chris (new)

Chris Aldrich (chrisaldrich) | 19 comments Theresa, Thanks for your note, but no worries. It's hard enough to get a book group together, much less one on mathematics, even when the interested people are highly motivated. Mathematics has always been a solitary effort and typically becomes even more so in the abstract areas. If cost is an issue, I can loan you a copy of my book for when you get a chance to get around to this. Dover also has some incredibly inexpensive and excellent texts in topology (and many other areas of math, science, and engineering as well).

As for myself, I've been doing some work in measure theory and Lebesgue integration since the beginning of the year and that combined with some work in information theory has kept me more than busy too.

If anyone is interested in pushing along with this topic, please feel free to chime in when you may have some time.


message 8: by Adam (new)

Adam | 19 comments I truly wish I had time to read Munkres' book. I've had it for a few years now, but between stuff I want to work on and my teaching load. It doesn't seem like I would get there for quite a while. It's very annoying.


message 9: by James (new)

James | 2 comments If this group gets going again, you can count me in. I have Munkres and several others. I used Munkres when I was in college. A good review would be nice.


message 10: by Ronald (new)

Ronald Lett (slider142) | 15 comments I am still up for this review as well. I haven't had a good in depth review of topology in quite some time.


message 11: by Prinn (last edited Jul 20, 2014 07:55PM) (new)

Prinn | 3 comments I have a question, and I am seeking mathematicians to help me answer it (I'm sorry if my question is off-topic).

I have a six year old son who is deeply mathematical. He has an almost mystical connection to numbers. I am looking for books for him. He is way beyond the children's books, but not yet interested in algebra, trig, or calculus. He likes integers, patterns, and geometry. Lots of pictures are good, but more advanced concepts than you find in the kids' books. He also loves clocks and planetary systems.

If you all have any suggestions I would certainly appreciate it.


message 12: by Adam (new)

Adam | 19 comments I really wish I had some ideas. It's almost like he might be ready for coordinate geometry, imposing geometric figures on a cartesian plane... which could lead to analytical geometry which connects geometry with algebra. Such a book would be beautiful if written for children...


message 13: by Ronald (last edited Jul 04, 2014 10:12AM) (new)

Ronald Lett (slider142) | 15 comments Vtfrank, I would recommend books along the lines of What Is Mathematics?: An Elementary Approach to Ideas and Methods and books on recreational mathematics, such as those by Martin Gardner. These types of books teach real mathematical reasoning and survey a wide swath of topics where the emphasis is on exploration, as it should be, instead of indoctrination in a particular subject. They are also very entertaining. :) In that vein, Stillwell's Mathematics and Its History can also help combat the sterile dullness that has seeped into the normal school mathematics curriculum.
Edit: From Sundials to Atomic Clocks: Understanding Time and Frequency seems to be a friendly introduction to the science of time as well.


message 14: by Prinn (new)

Prinn | 3 comments Thank you both for your recommendations; I will certainly look into these. We came across a book at Barnes and Noble called "Sacred Geometry" by Stephen Skinner. It is pretty squishy, but it has many pictures of shapes and formulae in nature. I find lots of books out there for mature mathematicians, but very few for little ones. Maybe one of you will decide to write one...

Thanks again!


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