[ugrads] Modeling Course in Spring (and more)

Hemanshu Kaul kaul at iit.edu
Mon Nov 10 17:37:55 CST 2014

Dear Students,

Some of you have been asking me about the modeling course (Math 486/522) in
Spring 2015. I am sending out this email with more information that should
be helpful to all of you.

As an aside, I am also teaching  Math 554 next semester which is a unique
course that introduces the use of tools and techniques from various fields
of mathematics like Probability, Linear Algebra, Algebra, Information
theory, etc. to existential and algorithmic problems arising in Graph
Theory, Combinatorics, and Computer science. If you have any questions
about this course, then don't hesitate to ask.

Regarding *Math 486/522*, I have completely re-done the course last spring
2014 and will be teaching the course based on this new structure and
syllabus (which will be made official after some tweaks next year).

The prerequisites are: Multivariable Calculus (Math 251), Differential
Equations (Math 252), Matrices and Linear Algebra (Math 332), plus
knowledge of basic Probability (What is probability/ Expectation/
Distribution?), and of any computing environment/ language like C, Java,
Matlab, etc.

The new course aims to develop an understanding of applied mathematics as a
thought-process and a toolbox for the study of real-world phenomena from
engineering, natural and social sciences, by learning concepts and tools
from different parts of mathematics – continuous, discrete, and
probabilistic – as they are applied to build and refine models for various
applications. Students will do a 8-10 week long project where they apply
the modeling process to analyze an open ended real-life problem, with a
deliverable of a project report and programming implementation.

The topics include:
1. Discrete change in financial and biological population systems –
equations and discrete dynamical systems, solutions and stability
2. Physical models – Proportionality and geometric similarity
3. Model fitting – Errors, Chebyshev criterion, least squares criterion,
regression, and data transformation
4. Discrete optimization models – Linear optimization, geometric and
solutions, integer programs and combinatorial optimization, binary
5. Network models – Graphs and networks, network flows, assignment problems,
graph coloring, vertex covers, local search algorithms
6. Discrete probabilistic models – Finite discrete time Markov chains and
stationary distribution, component and system reliability
7. Simulation Modeling – Monte Carlo algorithms, random point generation,
queuing models
8. Population models – Ordinary differential equations, equillibria, phase
and solutions fields
9. Competing species and predator-prey models – Dynamical systems, Euler’s
method, solving linear dynamical systems
10. Continuous optimization models – Multivariable optimization, gradient
Lagrange multipliers, Newton’s method
11. Special topics – e.g., complex network models, game theoretic models

With best regards,

Hemanshu Kaul
Associate Professor of Applied Mathematics
Illinois Institute of Technology

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