Course/Section

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Course Day/Time

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Instructor 

Math 4322 

Math 4322 

Course/Section

Class #

Course Title

Course Day & Time

Rm#

Instructor

Course/Section

Class #

Course Title

Course Day & Time

Rm#

Instructor

• An Introduction to Systems Biology, 2/e, U. Alon (an excellent, recently updated text on the “design principles of biological circuits”)
• Random Walks in Biology, H.C. Berg (a classic introduction to the applicability of diffusive processes and the Reynolds number at the cellular scale)
• Mathematical Models in Biology, L. Edelstein-Keshet (a systematic development of discrete, continuous, and spatially distributed biological models)
• Nonlinear Dynamics and Chaos, S.H. Strogatz (a very readable introduction to phase-plane analysis and bifurcation theory in dynamical systems with an emphasis on visual thinking; contains numerous applications in biology)
• Thinking in Systems, D.H. Meadows (a lay introduction to control systems and analyzing parts-to-whole relationships, their organizational principles, and sensitivity in their design)
• Adaptive Control Processes: A Guided Tour, R. Bellman (a classic, more technical introduction to self-regulating systems, feedback control, decision processes, and dynamic programming)

Course description: Topics in mathematical biology, epidemiology, population models, models of genetics and evolution, network theory, pattern formation, and neuroscience. Students may not receive credit for both MATH 4309 and BIOL 4309.

Instructor's description: An introduction to mathematical methods for modeling biological dynamical systems. This course will survey canonical models of biological systems using the mathematics of calculus, differential equations, logic, matrix theory, and probability.

Applications will span several spatial orders-of-magnitude, from the microscopic (sub-cellular), to the mesoscopic (multi-cellular tissue and organism) and macroscopic (population-level: ecological, and epidemiological) scales. Specific applications will include biological-signaling diffusion, enzyme kinetics, genetic feedback networks, population dynamics, neuroscience, and the dynamics of infectious diseases. Optional topics (depending on schedule and student interest) may be chosen from such topics as: game theory, artificial intelligence and learning, language processing, economic multi-agent modeling, Turing systems, information theory, and stochastic simulations.

The course will be taught from two complementary perspectives:

1. critical analysis of biological systems’ modeling using applicable mathematical tools, and
2. a deeper understanding of mathematical theory, illustrated through biological applications.

Relevant mathematical theory for each course section will be reviewed from first principles, with an emphasis on bridging abstract formulations to practical modeling techniques and dynamical behavior prediction.

The course will include some programming assignments, to be completed in Matlab or Python programming languages (available free through UH Software and public domain, respectively). However, advanced programming techniques are not required, and resources for introduction to these languages will be provided.

Text(s): Abstract Algebra , A First Course by Dan Saracino. Waveland Press, Inc. ISBN 0-88133-665-3

(You can use the first edition. The second edition contains additional chapters that cannot be covered in this course.)

Course description: Groups, rings and fields; algebra of polynomials, Euclidean rings and principal ideal domains. Does not apply toward the Master of Science in Mathematics or Applied Mathematics.

Other notes: This course is meant for  students who wish to pursue a Master of Arts in Mathematics (MAM). Please contact me  in order to find out whether this course is suitable for you and/or your degree plan. Notice that this course cannot be used for  MATH 3330, Abstract Algebra. 

Course description: Transformations, eigenvalues and eigenvectors.

Additional Notes: This is a proof-based course. It will cover Chapters 1-4 and the first two sections of Chapter 5. Topics include systems of linear equations, vector spaces and linear transformations (developed axiomatically), matrices, determinants, eigenvectors and diagonalization.

Instructor's Prerequisite Notes: MATH 6320

Supplementary (Recommended): Real Analysis: Modern Techniques and Their Applications, Gerald Folland (2nd edition); ISBN: 9780471317166.

Description: Lebesque measure and integration, differentiation of real functions, functions of bounded variation, absolute continuity, the classical Lp spaces, general measure theory, and elementary topics in functional analysis. 

Instructor's additional notes: Math 6321 is the second course in a two-semester sequence intended to introduce the theory and techniques of modern analysis. The core of the course covers elements of functional analysis, Radon measures, elements of harmonic analysis, the Fourier transform, distribution theory, and Sobolev spaces. Additonal topics will be drawn from potential theory, ergodic theory, and the calculus of variations.

While lecture notes will serve as the main source of material for the course, the following book constitutes a great reference:

• ”Statistics and Data Analysis from Elementary to Intermediate” by Tamhane, Ajit and Dunlop, Dorothy ISBN: 0137444265
• ”Applied Multivariate Statistics with R”, by Daniel Zelterman, ISBN: 9783319140926
• ”Applied Multivariate Statistical Analysis, sixth edition”, by Richard A. Johnson and Dean W. Wichern, published by Pearson.
• Rstudio: Make sure to download R and RStudio (which can’t be installed without R) before the course starts. Use the link R download to download R frst, then RStudio download to download it from the mirror appropriate for your platform.

Text(s):

• D.P. Bertsekas; Dynamic Programming and Optimal Con- trol, Vol. I, 4th Edition. Athena Scientific, 2017, ISBN-10: 1-886529-43-4
• J.R. Birge and F.V. Louveaux; Introduction to Stochastic Programming. Springer, New York, 1997, ISBN: 0-387-98217-

Additional Description: This course consists of two parts. The first part is concer- ned with an introduction to Stochastic Linear Programming (SLP) and Dynamic Programming (DP). As far as DP is concerned, the course focuses on the theory and the appli- cation of control problems for linear and nonlinear dynamic systems both in a deterministic and in a stochastic frame- work. Applications aim at decision problems in finance. In the second part, we deal with continuous-time systems and optimal control problems in function space with em- phasis on evolution equations.

• Peter Hoff (2009). A first course in Bayesian statistical methods. Springer
• Brian J. Reich & Sujit K. Ghosh (2019). Bayesian Statistical Methods. CRC Press.
• Christian P. Robert (2007). The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation. Springer (2nd Edition).

• We first convey the ideology of Bayesian statistics which is a particular approach to statistical inference that differs philosophically and operationally from the classic frequentist approach.
• We then define Bayesian inference and discuss its advantages. Detailed applications are illustrated using some classical models, including binomial, Poisson, univariate normal, multivariate normal model, and linear regression.
• We go through each step of building Bayesian hierarchical models and apply Bayes’ theorem to derive posterior distributions.
• To inference on posterior distributions, MCMC algorithm is introduced as a modern method of approximating posteriors