## Search found 30 matches

- Sun Aug 15, 2010 7:37 pm UTC
- Forum: Mathematics
- Topic: Math Books
- Replies:
**379** - Views:
**282408**

### 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...

- Mon Jul 26, 2010 3:03 pm UTC
- Forum: Mathematics
- Topic: Math Books
- Replies:
**379** - Views:
**282408**

### 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...

- Wed Jun 09, 2010 8:45 am UTC
- Forum: Mathematics
- Topic: Math Books
- Replies:
**379** - Views:
**282408**

### 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...

- Wed May 19, 2010 10:16 am UTC
- Forum: Mathematics
- Topic: Math Books
- Replies:
**379** - Views:
**282408**

### 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...

- Wed Feb 03, 2010 10:01 pm UTC
- Forum: Mathematics
- Topic: Double Majoring Physics/Math
- Replies:
**23** - Views:
**6853**

### 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...

- Fri Jan 15, 2010 6:36 am UTC
- Forum: Mathematics
- Topic: Real Analysis 1: What Topics Should Be Covered?
- Replies:
**9** - Views:
**1674**

### 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...

- Wed Nov 18, 2009 2:35 am UTC
- Forum: Mathematics
- Topic: Fundamental Theorem of Calculus
- Replies:
**16** - Views:
**2560**

### 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...

- 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:
**6785**

### Re: What is...

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

-romulox

-romulox

- Fri Aug 28, 2009 9:06 pm UTC
- Forum: Mathematics
- Topic: I may have actually made a useful function...
- Replies:
**20** - Views:
**2632**

### 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...

- Fri Aug 28, 2009 8:17 pm UTC
- Forum: Mathematics
- Topic: Struggling with the concept of compact space
- Replies:
**40** - Views:
**4137**

### 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...

- Mon May 25, 2009 7:56 pm UTC
- Forum: Mathematics
- Topic: Why is calculus considered so complex?
- Replies:
**64** - Views:
**7124**

### 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...

- Mon May 25, 2009 9:28 am UTC
- Forum: Mathematics
- Topic: Why is calculus considered so complex?
- Replies:
**64** - Views:
**7124**

### 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...

- Wed May 06, 2009 9:15 am UTC
- Forum: Mathematics
- Topic: Conceptual math (just a random thought)--
- Replies:
**13** - Views:
**1918**

### 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...

- Sat May 02, 2009 4:23 am UTC
- Forum: Mathematics
- Topic: Graph Theory Text
- Replies:
**3** - Views:
**495**

### 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...

- Mon Apr 06, 2009 7:16 pm UTC
- Forum: Mathematics
- Topic: What would I get in discrete math?
- Replies:
**15** - Views:
**2106**

### 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...

- Mon Mar 23, 2009 1:17 am UTC
- Forum: Mathematics
- Topic: Maths summer school - any ideas?
- Replies:
**13** - Views:
**2102**

### 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

-romulox

- Wed Mar 11, 2009 7:33 am UTC
- Forum: Mathematics
- Topic: Definitions & explanations in English/Actual uses for math
- Replies:
**19** - Views:
**1919**

### 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...

- Thu Dec 11, 2008 9:36 pm UTC
- Forum: Mathematics
- Topic: Re: Mathematics
- Replies:
**3** - Views:
**918**

### 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...

- Mon Dec 01, 2008 12:09 am UTC
- Forum: Mathematics
- Topic: ramsey theory
- Replies:
**3** - Views:
**1045**

### 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

-romulox

- Sun Nov 30, 2008 3:39 am UTC
- Forum: Mathematics
- Topic: ramsey theory
- Replies:
**3** - Views:
**1045**

### 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 ...

- Thu Aug 28, 2008 6:34 am UTC
- Forum: Mathematics
- Topic: Calculus Project
- Replies:
**17** - Views:
**1992**

### 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...

- Tue Aug 05, 2008 3:51 am UTC
- Forum: Mathematics
- Topic: Book on proofs?
- Replies:
**12** - Views:
**2155**

### 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...

- Mon Jun 30, 2008 8:05 am UTC
- Forum: Mathematics
- Topic: infinity
- Replies:
**91** - Views:
**10606**

### 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...

- Sun Jun 15, 2008 7:57 am UTC
- Forum: Mathematics
- Topic: Analysis Textbooks: Rudin vs. Buck
- Replies:
**11** - Views:
**2820**

### 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...

- Wed Jan 23, 2008 2:37 am UTC
- Forum: Mathematics
- Topic: Looking for Maths problems
- Replies:
**28** - Views:
**6056**

### 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

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

- Wed Dec 12, 2007 8:22 pm UTC
- Forum: Mathematics
- Topic: biography of godel
- Replies:
**5** - Views:
**1306**

### Re: biography of godel

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

romulox

romulox

- Wed Dec 12, 2007 5:41 am UTC
- Forum: Mathematics
- Topic: biography of godel
- Replies:
**5** - Views:
**1306**

### 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

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

thanks for the help.

romulox

- Wed Dec 12, 2007 5:32 am UTC
- Forum: General
- Topic: Who the dickens are you?
- Replies:
**10922** - Views:
**2411540**

### 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.

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.

- Wed Jun 20, 2007 7:08 pm UTC
- Forum: Mathematics
- Topic: math notation book
- Replies:
**4** - Views:
**2280**

### thanks

thanks. the list helps.

-romulox

-romulox

- Tue Jun 19, 2007 8:09 pm UTC
- Forum: Mathematics
- Topic: math notation book
- Replies:
**4** - Views:
**2280**

### 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

thanks

romulox