Search found 30 matches

by romulox
Sun Aug 15, 2010 7:37 pm UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 279254

Re: Math Books

grimreeker, i have not personally used Johnsonbaugh's book . i read a few amazon reviews which seemed to imply the book was not very good. sometimes you can find older editions of good books for cheaper. i am not saying rosen's book is the best, only that i have used it and that it is sufficient, br...
by romulox
Mon Jul 26, 2010 3:03 pm UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 279254

Re: Math Books

kenneth rosen's discrete mathematics and its application is pretty good. it covers most major and minor areas in discrete mathematics though you may have to find a good supplement for a sound treatment of first order logic and boolean algebra. The book does not cover most topics in any sort of depth...
by romulox
Wed Jun 09, 2010 8:45 am UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 279254

Re: Math Books

B.good, If you enjoy mathematics from an abstract perspective I would recommend Herstein's Abstract Algebra . The book is somewhat self contained (i.e. a thorough intro chapter to the basics) and has exercises at a few levels of difficulty. The book also provides a nice foundation for graduate books...
by romulox
Wed May 19, 2010 10:16 am UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 279254

Re: Math Books

As an undergraduate we used Herstein's Abstract Algebra (not to be confused with his Algebra). The book begins with basic ideas about sets and functions and gives a good undergrad introduction to group theory, ring theory and field theory. A few special topics are introduced at the end. One nice thi...
by romulox
Wed Feb 03, 2010 10:01 pm UTC
Forum: Mathematics
Topic: Double Majoring Physics/Math
Replies: 23
Views: 6793

Re: Double Majoring Physics/Math

Some US universities have an upper bound on the number of courses you can take at an in-state tuition rate. This may or may not be a factor for you. Since I had changed majors five times this was a consideration for me, and I was unable to double major in History and Mathematics (had to minor in his...
by romulox
Fri Jan 15, 2010 6:36 am UTC
Forum: Mathematics
Topic: Real Analysis 1: What Topics Should Be Covered?
Replies: 9
Views: 1641

Re: Real Analysis 1: What Topics Should Be Covered?

You may need to consider how the course will be taught. My first real analysis course covered sets, sequences, limits, functions, continuity and differentiation from scratch using the Moore method. The first day of class our professor handed out a sheet of theorems. The class would not get a new she...
by romulox
Wed Nov 18, 2009 2:35 am UTC
Forum: Mathematics
Topic: Fundamental Theorem of Calculus
Replies: 16
Views: 2542

Re: Fundamental Theorem of Calculus

The way we proved the FToC required the mean value theorem. The MVT only depends on the continuity of f though and could easily be proven (uses continuity,min-max thm, and fixed pt thm/intermediate value thm). I am not sure of the specifics of the historical development. Keep in mind, mathematics ha...
by romulox
Tue Sep 22, 2009 3:48 am UTC
Forum: Mathematics
Topic: What's the coolest thing you've ever learned in math class?
Replies: 58
Views: 6678

Re: What is...

Ramsey's theorem, or Godel's completeness and incompleteness theorems.

-romulox
by romulox
Fri Aug 28, 2009 9:06 pm UTC
Forum: Mathematics
Topic: I may have actually made a useful function...
Replies: 20
Views: 2592

Re: I may have actually made a useful function...

To the original poster, mathematics is something one must do carefully. You may or may not be brilliant and may or may not have discovered something interesting. Many of the people on this forum have done math carefully for quite a while and have come to realize many neat things they discovered when...
by romulox
Fri Aug 28, 2009 8:17 pm UTC
Forum: Mathematics
Topic: Struggling with the concept of compact space
Replies: 40
Views: 4098

Re: Struggling with the concept of compact space

Another way to think about compactness (albeit, not in complete generality) is to consider various equivalent statements for a particular space. In a metric space, compactness is equivalent to a set being closed and totally bounded which is equivalent to the set having the bolzano-weierstrass proper...
by romulox
Mon May 25, 2009 7:56 pm UTC
Forum: Mathematics
Topic: Why is calculus considered so complex?
Replies: 64
Views: 6757

Re: Why is calculus considered so complex?

What do you think about the Moore method specifically? From what I've heard, it seems unnecessarily restraining. Being presented axioms without motivation is just not how mathematics is actually done. I've had four courses which used the Moore method so far: Number Systems, 2 Analysis courses, Metr...
by romulox
Mon May 25, 2009 9:28 am UTC
Forum: Mathematics
Topic: Why is calculus considered so complex?
Replies: 64
Views: 6757

Re: Why is calculus considered so complex?

For me the term "good" as applied to mathematical skill is too ill defined. For one, there should be a distinction between proof based mathematics for college/university and above, and the calculating mathematics that is usually seen in American high school and equivalent. Regarding the pr...
by romulox
Wed May 06, 2009 9:15 am UTC
Forum: Mathematics
Topic: Conceptual math (just a random thought)--
Replies: 13
Views: 1875

Re: Conceptual math (just a random thought)--

To properly answer the question we must distinguish between mathematical objects and physical objects. Sometimes these are the same, sometimes not. The physical answer is that the distance from 0 to 1 inch and 0 to 2 inch are probably distinct, and if one repeatedly halves each as much as is physica...
by romulox
Sat May 02, 2009 4:23 am UTC
Forum: Mathematics
Topic: Graph Theory Text
Replies: 3
Views: 488

Re: Graph Theory Text

We used Introduction to Graph Theory by Douglas West, 2nd Ed. in my graduate course. The book is reasonably good, and offers quite a range of problems to work on. Our class only made it through the first four chapters though. It would probably be suitable for an undergraduate or intro graduate cours...
by romulox
Mon Apr 06, 2009 7:16 pm UTC
Forum: Mathematics
Topic: What would I get in discrete math?
Replies: 15
Views: 2086

Re: What would I get in discrete math?

You can also get neat stuff like: pigeonhole principle or ramsey theory (though probably not in lower level course), partial orders, inclusion-exclusion, combinatorial proof methods, recurrence relations, generating functions (these are bad to the bone), all sorts of nice things from Graph Theory, m...
by romulox
Mon Mar 23, 2009 1:17 am UTC
Forum: Mathematics
Topic: Maths summer school - any ideas?
Replies: 13
Views: 2086

Re: Maths summer school - any ideas?

You might try checking out the Mathworks program at Texas State University, link. They have been running summer math programs for pre-college students since at least 1990. Topics for the Honors summer program include things like Number Theory and Analysis. Hope this helps.

-romulox
by romulox
Wed Mar 11, 2009 7:33 am UTC
Forum: Mathematics
Topic: Definitions & explanations in English/Actual uses for math
Replies: 19
Views: 1891

Re: Definitions & explanations in English/Actual uses for math

I think it is good to remember that Mathematics is a process. In general, mathematics is the study of equivalence under particular assumptions. As we find more ways to characterize objects and relationships, some areas take on more emphasis. It is not as though one day there was not calculus and the...
by romulox
Thu Dec 11, 2008 9:36 pm UTC
Forum: Mathematics
Topic: Re: Mathematics
Replies: 3
Views: 910

Re: Mathematics

In high school I never took a course past algebra II. When I got to college I started as a creative writing major. I began taking computer science courses, two of which were discrete math courses covering boolean algebra, logic, etc... Those got me hooked, but the final blow came from a Number Syste...
by romulox
Mon Dec 01, 2008 12:09 am UTC
Forum: Mathematics
Topic: ramsey theory
Replies: 3
Views: 1035

Re: ramsey theory

Yeah I saw that one as well as Ramsey Theory by Graham and Rothschild on Amazon, but was looking for first hand feedback. Thanks for your help mathangelist, I'll definitely check it out.

-romulox
by romulox
Sun Nov 30, 2008 3:39 am UTC
Forum: Mathematics
Topic: ramsey theory
Replies: 3
Views: 1035

ramsey theory

I am looking for a good book on Ramsey theory. I am currently a grad student in math and took a course on Combinatorics. The course used Brualdi's Intro to Combinatorics which briefly introduces Ramsey theory but doesn't really develop it much. Are there any good texts which develop the theory in a ...
by romulox
Thu Aug 28, 2008 6:34 am UTC
Forum: Mathematics
Topic: Calculus Project
Replies: 17
Views: 1945

Re: Calculus Project

This may be too advanced but you could explore the necessary requirements for the fundamental theorem of calculus to hold. Or you could explore why continuity is not a necessary requirement for integration. Similarly, if continuity implies differentiability, is the converse true? Develop the propert...
by romulox
Tue Aug 05, 2008 3:51 am UTC
Forum: Mathematics
Topic: Book on proofs?
Replies: 12
Views: 2121

Re: Book on proofs?

heres a simple one. note: assume all sets non-empty. def 1a: Suppose S is a set. S is bounded above if there exists an M such that for every x in S , x <= M. def 1b: S is bounded below if there exists an L such that for every x in S , x >= L. def 1c: S is bounded if S is bounded above and bounded be...
by romulox
Mon Jun 30, 2008 8:05 am UTC
Forum: Mathematics
Topic: infinity
Replies: 91
Views: 10361

Re: infinity

how many axioms are required to consistently describe all of mathematics? is there a number to answer this question? should there be? Should observability be the sole measure of utility? i am of the view point that the human brain is capable of differentiating between a concept as a concept and a co...
by romulox
Sun Jun 15, 2008 7:57 am UTC
Forum: Mathematics
Topic: Analysis Textbooks: Rudin vs. Buck
Replies: 11
Views: 2768

Re: Analysis Textbooks: Rudin vs. Buck

Neither of the two analysis courses I took as an undergrad had a text. The professor taught using the Moore method and a constructivist approach and each week handed out a new sheet of theorems for everyone to prove. The pace was slow; we started with basic set theory, then sequences, limits, functi...
by romulox
Wed Jan 23, 2008 2:37 am UTC
Forum: Mathematics
Topic: Looking for Maths problems
Replies: 28
Views: 6018

Re: Looking for Maths problems

try this one

Suppose the function f is continuous on [a,b] and S={x in [a,b] : x=a or f([a,x]) is bounded}. Prove S = [a,b]. For some a,b in R. Use standard (accepted/appropriate for real analysis) definitions for continuous and bounded.


not too hard. not too easy.

-romulox
by romulox
Wed Dec 12, 2007 8:22 pm UTC
Forum: Mathematics
Topic: biography of godel
Replies: 5
Views: 1299

Re: biography of godel

thanks for the suggestions. i'll be certain to check them out.

romulox
by romulox
Wed Dec 12, 2007 5:41 am UTC
Forum: Mathematics
Topic: biography of godel
Replies: 5
Views: 1299

biography of godel

i am looking for a biography of Kurt Godel. Perhaps some of you could recommend something.

focus can be on math, logic, life, etc...

thanks for the help.

romulox
by romulox
Wed Dec 12, 2007 5:32 am UTC
Forum: General
Topic: Who the dickens are you?
Replies: 10922
Views: 2375276

Re: POST HERE FIRST - INTRO THREAD THE THIRD

romulox

finishing BS in Mathematics (last sem). looking forward to Ph.D. in Topology (probably Algebraic). interests in economics, history, computer science and english (all previous majors of mine :-/).

cheers.
by romulox
Wed Jun 20, 2007 7:08 pm UTC
Forum: Mathematics
Topic: math notation book
Replies: 4
Views: 2262

thanks

thanks. the list helps.

-romulox
by romulox
Tue Jun 19, 2007 8:09 pm UTC
Forum: Mathematics
Topic: math notation book
Replies: 4
Views: 2262

math notation book

Is there any text that contains a set of standard symbols and notations used in various fields of mathematics? i think i'm looking for a dictionary of math terms/symbols.

thanks

romulox

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