Mathematics Program at Biola University

Mathematics Undergraduate Catalog
Our Teaching Method.
No More Fears for Math.
What is so special about Math at Biola?
Some Highlights.

Math Is Fun.
There was a student Mike whose father said one day, "I have heard many things said about calculus, but. never have I heard one use the word fun to describe it, as my son said Dr Woo did." We have a lot of laughs in the classes, as exemplified by photographs of smiling faces, hysterical giggles, all over our wall boards. One unforgetable graduate was Sheila Ira, who had the knack of making mistakes creatively. In a Linear Algebra course, to save time, she simplified a matrix by simultaneously adding row 2 to row 3 as well as adding old row 3 to row 1. The result is a wrong matrix, but the mistake is so subtle that we called it Ira-ism, in honor of her. Another day she came in with a funny flabby double cube, made with coffee stirrer straws and dental floss. It was a correct but ugly model of a 4-dimensional cube, which we hung on our Departmental notice board for 2 years. I asked her did she want to bribe me for extra credit. She said unabashedly, "That is the idea." I like such students. Another student Brenda found a way to prove a certain matrix is equivalent to another, more elegant that I could do it myself. That technique was called, of course, Brenda-ism.

Our Teaching Method.
I remembered my undergrad math professor who avoided giving examples of things, so that our minds should be trained to " think abstractly". He also was proud of his ability to "make simple things complex". I am vowing to you that I shall do his opposite.

Here we teach math students, whether math majors or not, to express themselves clearly and succinctly in a universal language, with the right amount of formulas mixed with the right amount of sacred English phrases such as:

"Let x and y be any 2 elements of S", "Without loss of generality, assume A < B < C", "Suppose...", "Hence...", "if and only if", "By a stroke of genius, let us consider ... ", "QED".

No More Fears.
We will first of all get you to see the fun of math, the elegance of clever tricks, logical proofs, geometric diagrams, and funny things famous mathematicians did. That gets you over the phobia of mathematics and its proofs. Next, we get you to write elegant proofs yourself, which boosts your confidence. Students would exclaim, "I did it!." We encourage you do your homework in the afternoons at our "math lab", where some senior math student is there on most afternoons to help you.

Soon you will enjoy math as much as musicians enjoy music, and one of our past students had a lively discussion with a art student on whether fine arts or math has more beauty and elegance. We are not satisfied until you are so filled with enthusiasm to teach and share it when you graduate.

What is so special about Biola's math program?
First, the 3 full-time faculty members here are pretty well- round with all the main branches of undergrad math, Chairman Dr Walt Stangl is one of the most popular teachers of beginning Calculus. He also is very good on Math History, Number Theory, Probability and Statistics, and Topology. Our longest faculty Dr Ed Thurber is good in Number Theory, Algebra, Math History, Complex Variables, Numerical Analysis. Finally I myself, Dr Peter Woo, am excited about Geometry, Algebra, Differential Equations. All of us teach advanced calculus quite well. I am interested in Math History too, especially that in China.

Next, our graduates have no problem looking for jobs in teaching or go on with graduate school. We like to compare our curriculum with that of California State University systems, and we think that we do better in getting our students not just to master the skills of math, but the total picture if its role in science, in history, in philosophy, as well as its influence in shaping a proper personal self-image that is confident and not arrogant. We also find many humorous ways to blend in our Christian beliefs into the disciplines of math. I have a calculus problem that illustrates the efficacy of the substitutionary sacrifice of Jesus Christ.

Thirdly, you will not find so much opportunities to have < b>access to counsel and help from the faculty members in a university of tens of thousands of students, as here in Biola. We have seen not a few students, depressed and discouraged, over finance, parental divorce, or simply bad grades, that came to us in tears, and regained their confidence and strength as they walk out of our offices. I remember praying with a girl totally in tears, at finals week, whose book-bag with her ID cards and money was lost while left in a room. We sat down, prayed, and the next day somebody called her and said he took it by mistake. (How can one be so blind?)

Fourthly, we provide you with enough flexibility to pursue some private study-research course under faculty direction. We have enough computers that can run Mathematica and other software that provides full support for new textbooks that is more geared towards such software tools.

Some Highlights of What we Teach.

Calculus: We do teach hyperbolic functions and partial fractions using complex roots of quadratics. We also like to teach some differential geometry of curves and surfaces. We also teach coordinate geometry techniques in proving geometric properties of parabolas, ellipses, hyperbolas.

Linear Algebra: We teach you techniques of playing with matrices as well as abstract algebra concepts of vectors and vector spaces. We like to teach you geometric meanings of eigenvalues and eigenvectors. This is the course that give you an almost visual feeling of the reality of 4-th 5-th and higher dimensional spaces.

Discrete Structures: We teach you combinatorics, algorithms to find shortest paths in a graph, travelling salesman problem, and problems that are popular in the national Putnam Math Competition. I like to include with it Fibonacci series and stories of Erdos and other modern giants.

Geometry: We teach you 2 courses, covering concrete things that are either useful in daily lives or elegant, sometimes both. The courses are very enjoyable throughout the semester. We teach you all kinds of theorems on circles, on constructions with compass and with or without a ruler, on properties of tetrahedrons, on many centers of the triangle, e.g., orthocenter, centroid, incenter, Lemoigne center, Fermat center, Napoleon point, Feuerbach point, Euler line, Simpson line. We teach non-Euclidean geometry by deriving formulas of airplane navigation, areas of a triangle on the surface of the globe bounded by curves of great circles. We teach also projective geometry, elementary differential geometry, and inversions of a plane with respect to a circle.

Differential Equations: We teach you the graphic and philosophic interpretations of diff. eqns. in real life. We equip you with techniques of Laplace Transforms and Fourier series to solve 3-dimensional partial diff. eqns. in Physics, such as the wave equation, heat equation, Laplace equation. We also introduce you to methods of solutions using computers. That is the content of the other course:

Numerical Analysis: We teach you to use Mathematica and other software to solve differential or algebraic equations, and learn to estimate the stability and errors of the solutions. Math students are thus trained to do some computer programming and to appreciate algorithms.

History of Mathematics and Number Theory: This is a required course where we teach you appreciate the power and development of math in history, stories of famous mathematicians and their contributions, mathematics in ancient cultures such as the Mesopotameans, Egyptions, the Arabs, the Hindus, the Chinese. In Number Theory you will learn the Chinese Remainder Theorem, the Fermat Theorem, and the Prime Number Distribution Theorems.

Complex Variables: We teach you complex integration as well as geometry of complex numbers.