### 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.