SPIRIT OF ENQUIRY LECTURES IN MATHEMATICS

This concerns a proposal to hold lectures every Saturday at IIT(M) where the aim is to expose undergraduate students in Chennai to the ‘spirit of enquiry’ that is the core of mathematical discipline, by organising lectures which will cover more or less the B.Sc. syllabus, but in a more pedagogically appealing manner than the unmotivated recipes that are sometimes unfortunately dished out in undergraduate courses. We wish to emphasise that by having a clear understanding of the fundamentals, students can be better at, and enjoy much more, the material that is taught in their undergraduate classes.

We hope to also videograph these lectures and put them on an appropriate web-site so they could also be accessed by a much larger audience. This series of lectures will commence on Saturday the 29th of August 2009 in Lecture Theatre 1 on the third floor of the IC and SR building at IIT Madras.

To start with, we shall begin with two courses of lectures, which will meet every Saturday morning, as follows:

(I) Linear Algebra: (1000-1115);

lecturer: V.S. Sunder, IMSc.

The course will aim to convey various standard notions such as:

- vectors and linear geometry
- linear transformations, matrices, and their algebra
- systems of equations
- rank and row-reduction
- Range-nullity theorem
- canonical forms
- spectral theorem

(II) Calculus (1130-1245);

lecturer: Amritanshu Prasad, IMSc

The fundamental concepts of one-variable calculus will be discussed. Rigorous mathematical definitions and proofs will be presented in a clear manner, along with examples that illuminate these ideas. Main topics to be discussed are:

- Sequences
- series
- limits
- continuity
- derivatives
- Riemann integrals.