**Prerequisites: Instructor's permission**

**The contents for this semester**

This course would cover many basic topics and few important results in Mathematics related to

Operations research. The majority of the content (at least 60%) would be from ‘A First course in

optimization theory’ by Rangarajan Sundaram and the remaining portion would cover some math

basic tools required for Probability. Broadly it attempts to cover the following

• Analysis Sequences and limits, Open, closed, convex and compact sets, limit superior and

limit inferior, Matrices, Continuity and differentiability of functions, Intermediate and mean

value theorems, Implicit function theorem.

• Optimization Weierstrass Theorem, Theorem of Lagrange, Convex structures in optimization,

Kuhn and Tucker Theorems Parametric continuity: Maximum theorem

• Probability Monotone class theorem, Integration, and expectation, Some measure-theoretic

concepts, some more concepts related to probability theory.

If time permits might cover some important stochastic processes. And I might add/delete

some topics after discussing with the students in the first few classes.

The focus of the course could be on recent models, techniques computations, and/or applications.

__A selection from the following topics :__

* Advanced simulation techniques

* Conic programming

* Interior point methods

* Learning algorithms

* Martingale theory

* Queueing systems

* Stochastic games and stochastic control.

The specific topics to be covered in each offering of the course will be announced along with the instructors. Instructors can add a topic after informing IEOR department.

#### References

- Vivek S. Borkar, Stochastic approximations: A dynamical system viewpoint, 2008, Hindustan Book Agency, New Delhi TRIM series
- K. Talluri and G. van Ryzin, 2002, The theory and practice of Revenue Management, Kluwer, Amsterdam
- R. L. Phillips, Pricing and Revenue Optimization, 2004, Stanford Univ. Press, Stanford
- James Renegar, A Mathematical View of Interior-point Methods in Convex Optimization, SIAM, 2001
- Ronald Wolff, Stochastic modeling and the theory of qaueues, Prentice-Hall, 1989
- L.C.G. Rogers and D. Williams, Diffusions, Markov processes and martingales, Vols. 1 and 2 John Wiley & Sons, 1994
- Jerry Banks, Handbook of Simulation: Principles, Methodology, Advances, Applications, and Practice, Wiley, 1998.
- Open literature from journals and periodicals that exemplify the recent progress in the field of industrial engineering and operations research.

-----------