BSC4024103 Project Details
| Supervisor | Toh Pee Choon |
| Project Code | BSC4024103 |
| Title of Project | Introduction to Modular Forms |
| Description | It is well known that Andrew Wiles [4,3] proved Fermat's Last Theorem, i.e. the following Diophantine equation has no solutions in positive integers if n is an integer greater than 2. What may not be so well known is that Wiles' proof established a link between two vastly different classes of mathematical objects. He showed that a certain class of elliptic curves are related to modular forms. Our aims in this project are quite modest in comparison. We will learn about modular forms and how these complex analytic functions are connected to number theory. The main references are Chapter 3 of Koblitz [1] and Chapter VII of Serre [2]. |
| Pre-requisites | • Background in Abstract Algebra and Complex Analysis |
| References | [1] Koblitz, N., Introduction to Elliptic Curves and Modular Forms, Graduate Texts in Mathematics, 97 (1993). [2] Serre, J.P., A Course in Arithmetic, Graduate Texts in Mathematics, 7 (1973). [3] Taylor R., Wiles A., Ring theoretic properties of certain Hecke algebras, Annals of Mathematics, 141 (1995), 553-–572. [4] Wiles, A., Modular elliptic curves and Fermat’s Last Theorem, Annals of Mathematics,141 (1995), 443-–551. |