### Class Highlights

**Thur Apr 24**
Give back final project part 1.
Discuss review ideas for undergrad test
(review old WebCT quizzes,
know the info contained there (including basic contributions
of different cultures along with dates, and the history of the
topics we covered along with the dates)
and know Euclidean Geometry and
Non-Euclidean Geometry and the readings from the texts.)
Compare Euclid's Proof of Proposition 1 with
a modern version of the proof.
Discussion about homework readings. Discussion about the
changes in geometry over time. Recent developments in geometry.

**Tues Apr 15** Discuss the Parrot's Thm assignment.
Undergrads sign up for 10 minute conferences.
Grads turn in hw and tell us their choice for the grad review day.
WebCT test 5 on Calculus.
Go over web-based Euclid's elements.
Go thru the
Introduction,
Euclid,
and skim
A Quick Trip through the Elements (do not click on the sublinks).
Carefully read
Postulate 5
and
Proposition 1.
After reading this last web page, go back over it again, and write out
a modern proof of propostion 1 in your own words (using modern language too).
Be sure to include the justification for each step.
Then read
A Short History of Geometry.
Afterwards, go back through this link and use it to address how
the methods and philosophy of geometry have
changed over the years with examples (by referring
to specific people and their work) that illustrate these changes.
You may complete additional web research to help you.
When you are finished, turn in your work (proposition 1 and
the changes in geometry). If time remains, then work on
your final project.

**Thur Apr 17** Undergrads - 10 minute consultation with Dr. Sarah
in 326 Walker about the final project (see signup sheet on her door).
Grads - grad
review day with Dr. Rhoads.

** Tues Apr 8** Grad only day on DEs:
What is a differential equation?
History of ODEs
History of Differential Equations
Euler's Method in Pictures
Biography of Euler
Intro to Preditor-Prey Models
Read the history of preditor-prey models
Preditor Prey on Maple (Use ctrl / mouse click, then
download the link to the disk and save it as pp.mws. Then open it from
Maple).
html of the file
Intro to the Wave
Equation
History of Spectral
Theory
Take a look at the main web page, and read through the
final project info.

**Thur Apr 10** Go over worksheets from last Tuesday.
Discuss the final project.
History of geometry before Euclid.
Contributions from Egypt, Babylonia, India and Africa, and the early
Greeks. Intro to Euclid and Euclid's 5 postulates.

**Tues Apr 1** WebCT test 4 on algebraic structures and algebraic
geometry. Worksheet on the
history of derivatives
and Newton and Liebniz on derivatives

**Thur Apr 3** Calculus continued.
page 1
page 2
page 3
History of the propogation of calculus via Maria Agnesi.
History of rigour in calculus, analysis and topology.
Discuss of the final project.

**Tues Mar 25**
worksheet
Volume of a sphere
Volume
of a sphere (Cavalieri's principle)
Web activities on original sources for calculus.

**Thur Mar 27** Grad only day on calculus and analysis.
History of limits and analysis.

**Tues Mar 18**
Discussion based on questions about The Proof video.
Review Dr. Rhoads' history of algebraic geometry.
Dr. Sarah's Algebraic geometry worksheet.

**Thur Mar 20** Review the Algebraic geometry worksheet.
Intro to Calculus.

Spring Break

**Tues Mar 4**
Review the history of algebraic structures.
History of the connections between algebra and geometry, the split into
two separate fields, and algebraic geometry. Intro to Fermat's Last
Theorem.

**Thur Mar 6** Questions to think about during The Proof video.
The Proof video.

**Tues Feb 25**
WebCT test 3. Check WebCT mail to see whether your attachment came through.
If not, resend this ASAP.
Read ONLY up to the Fields section of
Galois Theory
Read
Progression of Solutions of Polynomials by Radicals to the beginning of
Modern Algebra
Dr. Sarah's Maple Quintic Demo
Dihedral group as the symmetries of a square
worksheet.
Worksheet on Galois and the pentagon.

**Thur Feb 27** Grad students only day:
Algebraic structures continued.
An overview of groups, rings and fields. An intro to Galois Theory.
Algebra versus Modern Algebra/ Abstract Algebra.
History of Modern Algebra.
Applications.

**Tues Feb 18**
Web searching.
Worksheets on
Diophantus,
False Position (Egyptian), Three Linear Equations (Chinese),
Quadratic Formula, Recorde, Rhind Papyrus.

**Thur Feb 20**
Grad students only day:
History of Matrices and Determinants
A Brief History of Linear Algebra and Matrix Theory
Introduction to Olga Taussky Todd and the
Gerschgorin Circle Theorem

**Tues Feb 11** Collect remaining worksheets.
Go over the p = 3 in the bible controversy
and a method to see whether Apu is correct from the
Pi
worksheet.
Review Cantor's Diagonal argument to show that there are more
real numbers than there are natural numbers, and then use the argument
to show that the rational numbers are enumerable.
Discuss entry on Hypatia on p. 123 of the Parrot's Theorem
and the related upcoming assignment from the Parrot's Theorem (once we
finish reading the book).
Take questions on the homework book readings.
Discuss the timeline assignment.
Finish up the history of numbers via the history of complex numbers.

**Thurs Feb 13** Hand back the homework and make some comments
about it. Then discuss the readings from the Burton book which pertained
to the methods of solving linear equations in ancient Egypt and Babylon.
Talk about solving a system of linear equations. Mention the Arithmetica
by Diophantus and the advances in it, then talk about how Indian mathematicians
solved quadratics.

**Tues Feb 4**
Go over irrationality of pi and introduce cantor's diagonal argument
that there are more real numbers than natural numbers.
Take WebCT test 2.
Pi
worksheet,
Georg Cantor reading,
Dodge Ball worksheet,
Cantor's Diagonal
Argument reading part 1
Cantor's Diagonal Argument reading part 2.

**Thurs Feb 6**
Grad only class day:
Proof of the irrationality of Pi,
discussion of algebraic and transcendental numbers,
discussion of countable and uncountable sets, Cantor ternary set.

**Tues Jan 28** Go over History of Math quiz web searching
results. Highlight diverse viewpoints, issues relating to the
reliability of references,
and other interesting issues that came up. Collect History Quiz web
searching homework.
Discuss WebCT test issues (boxes mean choose all that apply,
study suggestions, and curving the first quiz).
Take questions on the Parrot's Theorem readings. Collect grad student
homework on this after asking them to be sure to clarify whether
they came up with the info themselves or from another resource.
15 minutes to finish up the
Hypatia worksheet.
If finished early, then continue reading the Parrot's Theorem.

Discuss current research
in history of math via

**attempts to discover Hypatia's mathematics,
reliability issues via rumors regarding hypatia
and the "picture" of her,
(the
source of the misinformation on Hypatia).

**Archimedes "The Method of Mechanical Theorems",

Archimedes scholar finds something to holler 'Eureka!' about

Ivars Peterson's MatheTrek: Ancient Infinities
and

Scholars decode ancient text, shake up pre-calculus history
and

**
Martha Euphemia Lofton Haynes,
the first
African American woman mathematician (compare to the poster outside
of Dr. Sarah's office).

In the time that remains,
Dr. Rhoads begins the next topic.

**Thur Jan 30**
Prime number, composite number, perfect number. Prime game.
History of these. Euclidean algorithm and Euclidean statements.
Sieve of Eratosthenes, the number of primes, gaps between primes,
perfect numbers.

**Tues Jan 21**
Intro to WebCT, the bulletin board, and WebCT tests. WebCT test 1.
Intro to web searching.
Use the web to search for the answers to the History Quiz from
last Tuesday.
Finish worksheet from Thursday. If time remains then take WebCT survey.

**Thur Jan 23** The University Cancelled Classes

**Tues Jan 14**
Intro to the syllabus via web readings. Intro to the course.
Fill out information sheet.
History Quiz
(students will search for the answers next Tuesday).
Early History of
Mathematics video (30 minutes).

**Thur Jan 16**
Discuss homework reading and the
Early History of
Mathematics video.
Hypatia and Archimedes' Dimension of the Circle
activity sheet by Dr. Sarah and Edith Prentice Mendez.
If time remains, then begin reading the Parrot's Theorem.