This page collects the materials I designed for the undergraduate class Math 035 General Views in Mathematics at PSU. The course syllabus is here.

Slides

Ancient Mathematics: Greek, China and Arabia

Greek: the system of axioms

1.1-1.2 Euclid and plane geometry

1.3 Pythagoren Theorem

1.4 Hippasus

China: primal mathematics used in ancient engineering

1.5 Liu Hui, rod calculus and the computation of $\pi$

Arab: math ancient astronomy

1.6 Al-Kharizmi

1.7 Khayyam

Modern Mathematics

France

2.1 Descartes and the idea of modern geometry

2.2 Laplace and the origin of modern mechanism

2.3 Galois and the concept of group theory

Germany

2.4 Euler and topology

2.5 Gauss

2.6 Cantor and the discussion of real numbers

2.7 Klein and the early development of the international mathematica society

2.8 Leibniz

Russian and former USSR

2.9 Lobachevsky and a first course on non-Euclidean geometry

2.10 Kolmogorov

Weekly Assignments

1. Study the numbers of a language that is neither English nor your mother language, then write down the following numbers in this language: 0, 1,2,3,4,5,6,7,8,9,10,100,1000.

2. Buffon’s needle experiment This is a famous experiment of math by French mathematician Buffon. Follow the given steps on a piece of blank paper and write your answers: a. Paint a series of parallel lines equidistantly (i.e., each pair of adjoint lines keep a constant distance x) on the paper. b. Take a needle which is shorter than x. Randomly throw the needle onto the paper for n times. Count the time that the needle is intersecting with any line and denote it as m. The larger n you take, the better accuracy you will obtain. c. Compute the value of m/n. How do you think about it? What would we get if n is infinitely large?

In this mission, you could cooperate with others, but please finish the submission by yourself.

1. Ancient architecturers use the following method to measure the height of a mountain without climbing up to it. Choose a sunny day and measure the following values using a long soft ruler or other tools: a. Your height b. The length of your shadow c. The length of the shadow of the building Note that b and c shall be measured at the same clock. Otherwise you will lose accuracy. Finally, the height of the mountain=c*a/b.

Use this method to measure the height of any building in University Park. Write down the time (clock and date) of your work, your results of a,b,c and the height of your building.Attach a photo of the building in your file.

In this mission, you could cooperate with others, but please finish the submission by yourself.

1. Watch the film The Imitation Game. What is the math area involved in this film?

2. Watch the film The Man Who Know Infinity. Upload two screenshots when the characters are discussing math in the film.

Group Assignment Guidance

The interview project