MATH 480 - Senior Seminar

Current Office Hours: MW 11:30-12:20; W 2:30-3:20 (starting February)

 

Resources

Handouts

Books Online

TeX/LaTeX

Class Syllabus (in pdf form)

(Here it is as a LaTeX file)

Guentner's Math 480 calc review notes

H.B. Phillips, Differential Calculus, Wiley, 1916:

H.B. Phillips, Integral Calculus, Wiley, 1917:

One learning outcome of this course is experience writing mathematics using TeX or LaTeX. To use LaTeX you need a computer, a LaTeX compiler installed on that machine, and a text editor or editring environment in which to write your TeX file:
  • For Mac OS X users, I suggest MacTeX.
  • For Windows users, I suggest proTeXt, which is a special installation of MiKTeX.
  • For Linux/Unix users, the standard is TeX Live. (Your Linux installation might already have LaTeX installed!)
  • Rumor has it that there is also a cloud-based LaTeX for iPads and Android tablets, I will try to find out more about it.

There are many TeX guides and tutorials on the web, here are a few:Please email me if you have trouble with the installation, and I'll help you to sort it out.

  1. The Not So Short Introduction to LaTeX
  2. Wikibooks LaTeX intro. (See especially the section on Advanced Mathematics)
  3. more to come

Once you have LaTeX installed on your machine, you may use any text editor to write TeX files. However, you might prefer something like an integrated LaTeX environment, say, TeXShop (Mac), TeXWorks (Windows), or Kile (KDE). The proTeXt package for Windows installs a package called the TeXnicCenter, which is said to be very nice. Here is a comparison of various TeX/LaTeX editors.

I will soon post some sample TeX files.

Assigned Due Assignment
Jan 15 Jan 22 I. Review the following concepts from Calc I:
  1. Limits
  2. Continuity
  3. Differentiation
  4. Mean Value Theorem, Intermediate Value Theorem, Extreme (or Maximum) Value Theorem

(Problems to be assigned)

II. Decide how you will get access to LaTeX

Jan 22 Jan 27 Write a TeX document that says "Hello World! My Name Is <<your name here>>!". Email me the actual TeX file from this.

Practice Exam I: 3,5

Practice Exam II: 5,11

"Continuous Functions" handout: Read. Work problems 2-5

IVT and Bolzano" handout: Read.

Don't hand in these problems, but do work them and write them up. I'm going to have you discussing them in small groups then presenting them.

Jan 22 Jan 27 Look over the current state of this calculus topics page (based on our class discussions), and try to think of what we might have left out.

It will grow over time.

Jan 27 Jan 29 Come up with more topics to fit into the calculus topics page from the previous line (the one I handed out in class).
Jan 30 Feb 5 Here are two min-max problems from calculus. I want you to do careful solutions, and write them up in LaTeX:

The pdf

The simple LaTeX file used to create them

The picture I used in the file

Feb 10 Feb 12
  • Identify at least 8 of the problems from the Calc III (Math 252) final exam I gave you last week that you would be willing to work in class (on Feb 19). At least 4 of these must be from problems 9-15.
  • Also, identify any problems from this exam which you would like to see solved.
  • (Write these up for me, turn in Wednesday beginning of class.)
  • Try to remember what topics you discussed in Calc III-IV
March 5 Quiz on Calc III.
REMINDER: ATTENDANCE IN CLASS IS MANDATORY, NOT OPTIONAL.
March 10-12 Joint with other class, we will have a short review of countability (and more general cardinalities), and then explore transfinite induction.
March 12 Homework due March 19:

These problems on Math Induction.

Two problems chosen from problems 1, 3, and 4 in the handout from today's talk on cardinality. (In other words, do either 1&3, 1&4, or 3&4, don't do all three.)

You can turn these in on March 21 ()by email) instead of March 19 in class, but then I would like your solutions typed up in LaTeX.

March 17 Library tour. Meet in Room A156 Hamilton (1st floor addition)
March 19 We will have a guest speaker on the ``P=NP" problem. (Some people think this is the most important open problem in mathematics.) Attendance is mandatory, and I will ask you to write up a report on this talk. Instructions will appear here in the next few days.

HERE THEY ARE

Some reading for the next couple of weeks. You should find this fun and not hard. There is a password, it is Math480:

T.C. Mits Book 1

T.C. Mits Book 2

For each of the two volumes, I want every one of you to come up with at least 2 questions or statements (maybe a sentence or two each question/statement) around which we can structure a discussion. I will want you to send me these by the Wednesday after break. You can work together, but if you do then I still need separate questions/statements from each of you (for example, if 2 of you work together I expect a total of 8 such questions/statements from the two of you).

INSTRUCTIONS FOR THE FINAL PROJECT
Research practice exercises:

Problem 1: Find out what an "Erdos Number" is. Find the Erdos numbers for two UH math professors, past or present. (Not me; by the way, I believe my Erdos number is 3.) Prove your result by giving citations to the relevant joint papers. (Also, the abstracts if available.) Extra credit if one of these is a member of the department with an Erdos number of 1!

(Interestingly, the UH-Manoa VCAA also has a relatively low Erdos number. What is it?)

Problem 2: Using "mathematical genealogy," connect one of your UH math professors to one or more of the following:

  • Lagrange
  • Laplace
  • Euler
  • Weierstrass
  • Klein
  • Bolzano

Notes on the Banach-Tarski Paradox