Department of Mathematics April 29, 2016 with numerical methods in medieval Muslim mathematics, up to ... the court of the learned Maharaja Sawai Jai Singh in western India. ... Professor

UNDERGRADUATE MATH SEMINAR

The Hindu-Muslim Relations, Courtly Patronage, and Related Numerical Methods for Computing sin(1o) Early Modern Central/South Asia

Abstract: Before the development of power series expressions for trigonometric functions and electronic devices for evaluating them, the computation of accurate sine values required a great deal of mathematical creativity and ingenuity as well as hard work. This story, with elements of interest for both mathematicians and non-mathematicians, begins with the invention of trigonometry in the Hellenistic world and continues through the skillful blending of classical geometry with numerical methods in medieval Muslim mathematics, up to an account of a recently (re)discovered Sanskrit manuscript from the early 18th century. As our discussion will show, this manuscript reveals an intriguing instance of scientific transmission and mathematical synthesis at the court of the learned Maharaja Sawai Jai Singh in western India.

The next seminar of the term will DATE: TUESDAY, May 3 Time & 4:45pm – Refreshments in Bailey 204 Location: 5:00pm – Seminar in Bailey 207 In this seminar, Professor Kim Plofker from the Union College Math Department will present the following talk:

Professor Kim Plofker

Last spring, when I was choosing my thesis topic, I also made another decision, that is, applying for a computer science master program for my graduate study. I began to look at thesis topics that were related to applied mathematics or had some computer science involved in them. Ultimately, I got into my top choice, Clinical Evaluations of Spatially Registered Ultrasound Imaging under the direction of Professor Jue Wang. This ongoing research was mainly aiming to utilize the Backscatter-Contour-Attenuation (BCA) reconstruction method in ultrasound images to acquire more accurate contours of the prostate gland. These contours can then be applied to the medical plan for curing prostate cancer. Due to the complicated background knowledge necessary for this research, including medical knowledge, statistics theory, and image processing methods, the beginning of our first term of this two-term thesis mainly focused on learning all of the required basic knowledge. I had taken an introductory statistics course two years ago. Learning how to analyze the performance of the BCA algorithm reinforced my understanding of Root Mean Squared Error, Pratt’s Figure of Merit, Attenuation artifact correcting power, and etc. In the following part of my thesis, we mainly focused on optimizing the initialization process of the BCA method. Our goal was to make the prostate center our initial point in our algorithm instead of

Pieces from Thesis – by Shihui Xia ‘16

(Continued on next page)

Shihui’s thesis was supervised by Professor Jue Wang.

Department of Mathematics April 29, 2016

This week’s problem: Find the product of the real roots of the equation

x2 +18x +30 = 2 x2 +18x + 45 Professor Friedman will accept solutions to this problem until noon on Thursday, May 4.

randomly picking a pixel in the image. At first, Professor Wang suggested that I study a novel partbased Histogram of Gradient (HOG) based Support Vector Machine (SVM) detection approach mentioned in an IEEE paper. All of these concepts were new to me, and the instruction about the method in the paper was too general to be followed. After reading several relevant papers and discussion with Professor Wang, we got more detailed information from the author by email. Then, according to the analysis of performance using different values in the HOG based SVM method, we optimized the prostate center detection approach. We finally tried to simulate the approach in the second term with matlab using the ultrasound image data that we generated from our prostate phantom model. However, the result was disappointing. Before changing the method, we analyzed the cause of our failure with experiments that examined the significant factor that affected the HOG features, shape. In the last three weeks of my thesis, we studied a new image feature, Local Binary Pattern (LBP), which aims at texture classification. After some additional research, we believed that combining LBP with HOG features would improve the performance of the prostate center detection method. The thesis experience gave me a chance to practice the knowledge I have learned in class. It also let me experience the combination of math, computer science and even medicine. Also, I greatly deepened my research expertise and realized how important it was to improve my self-studying and problem-solving abilities. Now, I feel more confident to continue with graduate study in a totally different, unfamiliar area with my mathematics background. Finally, my suggestion for underclassmen is to choose the thesis topic that you think is interesting, and for them not be afraid of failures and challenges. You have the ability to overcome them and will get a great feeling of accomplishment once you conquer them. You will realize studying mathematics for undergraduate study is an excellent decision.

Problem of the Newsletter - April 29, 2016

Math on a Bridge

I saw the following picture that includes the equation contained in the famous Mean Value Theorem posted on Facebook. Supposedly, the bridge in this picture is in Beijing, China. I was wondering if anyone who reads this newsletter has seen this in person and/or knows the history behind the inclusion of this equation on this public work. If you are such a person, please send me an email about this!

-Paul Friedman ([email protected])

Page 2