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Mathematical Foundations for Big Data (Spring 2016)

MF 1:30pm-3:00pm, 2112 Math. Sci. Bldg.

Instructor: Thomas Strohmer

See https://www.math.ucdavis.edu/~

Course Objective:

Experiments, observations, and numerical simulations in many areas of science nowadays generate massive amounts of data. This rapid growth heralds an era of "data-centric science," which requires new paradigms addressing how data are acquired, processed, distributed, and analyzed. This course will cover mathematical models and concepts for developing algorithms that can deal with some of the challenges posed by Big Data.

Prerequisite:

- Linear algebra and a basic background in probability as well as basic experience in programming (preferably
- Matlab) will be required. Some basic knowledge in optimization is recommended.

- Principal Component Analysis, Singular Value Decomposition.
- Probability in high dimensions. Concentration of measure, matrix concentration inequalities.
- Curse of dimensionality.
- Data clustering, community detection.
- Dimension reduction. Johnson-Lindenstrauss, sketching, random projections.
- Compressive sensing. Efficient acquisition of data, sparsity, low-rank matrix recovery.
- Stochastic gradient descent.
- Kernel regression.
- Randomized numerical linear algebra.
- Diffusion maps, manifold learning, intrinsic geometry of massive data sets.
- Some basics on Deep Learning (if time permits).

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ECS 253 / MAE 253: ``Network Theory and Applications"

Instructor: Raissa D'Souza (raissa@cse.ucdavis.edu)

Time: Tues and Thurs, 4:10 - 6pm

CRN: 63626 (MAE) (If you want to register via the ECS listing, please email me.)

Location: 101 Wellman

Course description: Network structures are pervasive in the world around us, from the Internet and the power grid, to social acquaintance networks, to biological networks. This course is intended for graduate students interested in learning the modern science of networks, and should allow students to incorporate network theory into their own research. This course will cover general techniques and selected applications. Applications selected will reflect student interest, hence, to have input on which topics will be covered, please email the instructor. Suggestions encouraged!

Prerequisites. Familiarity with: linear algebra, basic statistics, calculus, ordinary differential equations, using computer software.

For more information see the course page from the 2014 offering:

http://mae.engr.ucdavis.edu/

General techniques:

- Graph theory

- Connectivity matrix and eigenvalues

- Models: random graphs, preferential attachment, optimization

- Topological features: degree distributions, small-worlds, power-laws, hierarchy

- Visualization software

- Data analysis

Sample applications:

- Immunology/epidemiology/

- Social networks

- Biological networks

- Design of transportation/distribution networks/energy networks

- Internet growth and modeling

- WWW search engines

- Self-organization and sensor networks