OAKLAND UNIVERSITY

DEPARTMENT OF MATHEMATICS AND STATISTICS

ADVISING NEWSLETTER

WINTER, 2000 -- Volume 5, Number 2

Become a mathematics tutor

The Academic Skills Center (103 NFH, 370-4215) needs your help! Mathematics tutors are in short supply. If you've had several mathematical sciences courses at OU and want to help your fellow students (while at the same time gaining valuable experience and earning a little spending money, with very flexible hours), give them a call. They also need good math students to serve as Supplemental Instruction leaders.

Special courses in spring and summer

We do not usually offer many advanced courses in the Spring or Summer terms (although APM 257 and MTH 256 do show up). This spring we have an advanced statistics course in repeated measures and mixed models taught by Professor Kushler. Please speak to the instructor for more details, including prerequisites.

Math professor honored

Professor Darrell Schmidt received the 1999 Oakland University Teaching Excellence Award. Each year one member of the OU faculty is honored in this way, and we are very proud of Professor's Schmidt's selection. Previous recipients in the Department have been Professors Downing and Grossman.

And after you graduate?

Many opportunities are open to you after you complete your undergraduate major in mathematics or applied statistics. One thing to consider seriously is graduate school. Here at Oakland University we offer several different masters degrees in mathematics and applied statistics, and our new PhD program in the applied mathematical sciences might be appropriate for you. Contact the Coordinator of Graduate Programs, Professor Kevin Andrews (andrews@oakland.edu, Room 548 SEB, 370-4025), for more information, and/or visit the departmental Web site (http://www.math.oakland.edu).

Early Registration coming

Here's a rundown on the advanced undergraduate courses being offered Fall 2000, as you continue thinking about your course selections. Early registration starts in May. Remember that courses are listed by rubric rather than by department, so you will have to look in separate parts of the booklet for APM, MOR, MTH, and STA offerings.

APM 332: Applied Matrix Theory (Kulkarni, MW 5:30 PM)

If you liked MTH 256, then you'll like this course, which goes into more depth on these topics

APM 433: Numerical Methods (Jiang, MW 7:30 PM)

Numerical analysis and scientific computing are important topics for you to know if you plan to seek a job in industry. Professor Jiang (bjiang@oakland.edu, 347 SEB, 370-3446) is one of the leading experts in the country on these topics. See him for what background you need to bring to the course.

APM 463: Graph Theory and Combinatorial Mathematics (Kulkarni, MW 7:30 PM)

If you liked discrete mathematics (APM 263), then you'll like this course, which goes into more depth on these topics. Many of the students in the class are graduate students in computer science, but mathematics majors tend to do just as well as, if not better than, these students.

APM 477: Computer Algebra (C. Cheng, TuTh 5:30 PM)

This course explores the mathematics behind the algorithms used by computer algebra packages such as Maple and Mathematica. The course is offered about once every two years.

MTH 302: Introduction to Advanced Mathematical Thinking (Schmidt, TuTh 3:30 PM)

Many advanced mathematics courses deal with why things are true, not just getting answers to problems. In this course you will become proficient in understanding and writing proofs. It is required for math majors and prerequisite to many advanced courses.

MTH 351: Advanced Calculus I (Shi, TuTh 3:30 PM)

This course, required of all math majors, explores calculus from a deeper and more theoretical point of view.

MTH 361: Geometric Structures (Tsui, MW 3:30 PM)

The Euclidean geometry you learned in high school is not the only interesting or useful way to model space. This course, required of math majors in STEP (and an elective for other math majors), looks at some of the alternatives.

STA 322: Regression Analysis (Khattree, MW 7:30 PM)

If you liked STA 226, and especially the time spent studying linear regression and correlation, you should look into this course. All statistics majors must take this course, and it is an elective for math majors. It is recommended that you have seen matrix operations (like multiplicative inverses) before.

STA 427: Introduction to Mathematical Statistics (Ogunyemi, MW 5:30 PM)

This is the first half of a year-long sequence in the theoretical foundations of probability and statistics, required of all statistics majors and an elective for math majors.

In all cases, you can obtain further information by talking to the instructor.

If you have a request for future years, make your desires known to us! Also, don't forget that you can do independent studies of topics not regularly offered as courses. And if you meet the prerequisites, consider taking graduate courses or advanced computer science courses, such as MOR 558, MTH 551, MTH 571, STA 506, STA 522, STA 530, STA 614, or CSE 343 (to mention those that are being offered next Fall).

Math conferences

On May 5-6 at Central Michigan University in Mt. Pleasant, the annual meeting of the Michigan Section of the Mathematical Association of America is being held. Students are encouraged to attend (there is no registration fee), and there will be sessions for student papers, as well as many talks and workshops accessible to undergraduates. Details can be obtained from Professor Grossman or (when it becomes available) on their Web site: http://www.michmaa.org.

Mathematics major David Houston presented a talk on "A Density Problem Related to Delay Differential Equations" at the Michigan Undergraduate Mathematics Conference at Alma College on February 19. Plan on attending next year, and even giving a talk -- no one bites and it's a great experience.

Contact information

The Newsletter editor is Professor Jerrold Grossman, the chief undergraduate adviser in the Department. We welcome your comments and suggestions; in fact, we welcome your contributions of material, if there's something you'd like to share with your fellow majors.

The department's Web Page ( http://www.math.oakland.edu) has lots of useful information about our programs, mathematics, careers, and lots more. Take some time to explore it!

All faculty have e-mail addresses that are the same as their last names (followed by @oakland.edu), with certain exceptions: bjiang, echeng, pshi, schochet, and w2zhang. Phone numbers and office locations can be obtained from the Department office (368 SEB, 370-3430) or the Web.

Come to a math talk!

Every week or two the Department holds a Colloquium, in which a mathematician or statistician (either someone in the Department or a visiting dignitary) presents a talk on recent progress in some area of mathematics or statistics. Colloquium announcements, which describe the subject and the speaker, are posted on the bulletin boards near the departmental office and on the Web. You may not understand all the details, but you can get a good feeling for what research in the mathematical sciences is all about by dropping in. Free refreshments are served prior to the talks.

Keep the advisers busy

Majors in mathematics or statistics should consult with their advisers at least once a year. Professor Grossman is currently the departmental chief adviser, and he can be found in Room 346 SEB most of every day (370-3443, grossman@oakland.edu). Sit down with him to review your progress, check the myriad graduation requirements, explore your options after you graduate, or just talk about mathematics. He has some nice give-aways, too, such as a booklet prepared by the Mathematical Association of America spotlighting careers in the mathematical sciences, and copies of recent issues of Math Horizons, a magazine for majors.

Summer opportunities

Each summer at numerous sites around the country, talented mathematics and statistics majors take part in programs, funded by the National Science Foundation, which allow them to do real mathematical research. Room and board are paid for you, and you receive a small stipend in most programs. You should seriously consider participating in one of these programs.

A few of these programs are specifically designed to encourage women in mathematics. There are also some that include course work as well. For more details, see Professor Grossman or check out this Albion College Web site: http://spider.albion.edu/fac/math/opportun.htm.

Another activity you might consider for the summer is being a tutor in our Summer Mathematics Institute for high school students; see its Web page (http://www.math.oakland.edu/ousmi.html) for details.

A personal look

Each issue of the Newsletter will include a feature on one member of the Department faculty, telling you a little about his/her life and interests, both professional and personal. We are proceeding by seniority at Oakland, and with this issue we come to Professor Charles Cheng, who has been at Oakland since 1975. He did his undergraduate work in Taiwan and received a PhD in mathematics from Rutgers University. He also took a leave from Oakland in the 1980s to earn a masters degree in computer science from the University of Michigan and work for a time at Bell Labs in Ohio.

Dr. Cheng's research interests revolve around abstract algebra, and especially computer algebra (the ideas behind software such as Maple and Mathematica). He has published many research papers, mostly in prestigious journals such as the Proceedings of the American Mathematical Society. While he has taught a wide range of courses at OU, these are also his favorite instructional areas.

In addition to his academic duties, Professor Cheng currently serves as associate chair of the Department. He is responsible for scheduling classes, handling student concerns, supervising the teaching assistants and parttime instructors, and keeping track of official departmental actions.

When not working on mathematics, Dr. Cheng is involved in music (he plays the violin and has performed with the Pontiac-Oakland Symphony) and local church activities.

Professor Cheng lives with his wife, Mei, in Rochester Hills. Mei works as a technician in OU's Eye Research Institute, helping with the gene therapy research going on there. They have two sons, both of whom were award-winning pianists in high school, and who now are engineering majors at UM and OU.

Math problems to try

Here are three of the problems from this year's Michigan Mathematics Prize Competition. Give them a try.

1. A 6-by-6 checkerboard is completely filled with 18 dominoes (blocks of size 1-by-2) Prove that some horizontal of vertical line cuts the board in two parts but does not cut any of the dominoes.

2. You run a boarding house that has 90 rooms. You have 100 guests registered, but on any given night only 90 of these guests will show up. You don't know which 90 it will be, but they'll arrive for dinner before you have to assign rooms for the night. You want to give out keys to your guests so that for any set of 90 guests, you can assign each to a private room without any switching of keys. You could give every guest a key to every room, but this requires 9000 keys. Find a way to do this with the smallest number of keys necessary so that each guest will have a key to a private room.

3. (a) The midpoints of the sides of a regular hexagon are the vertices of a new hexagon. What is the ratio of the area of the new hexagon to the area of the original hexagon?
(b) The midpoints of the sides of a regular n-gon (n > 2) are the vertices of a new n-gon. What is the ratio of the area of the new n-gon to that of the old? For both parts, justify your answer and simplify as much as possible.