Resume
Graduate Course Work, Topics & Highlighted Projects
- High Performance Computing
- Textbook: Using OpenMP by Chapman, Jost, Van Der Pas && CUDA by Example by Sanders and Kandrot
Main Topics: Single core cache-based performance optimization, Introduction to Message Passing: MPI, Non-blocking MPI point-to-point communication semantics in depth, Strategies for parallel solution of explicit and implicit PDEs, Nearest neighbor ghost cell filling for discretized PDEs, MPI Collectives, Techniques for "one-sided" programming for unpredictable communication, Techniques for implementing domain decomposition for particle codes, MPI User defined types, N-body problems, On-core Threading: OpenMP and Pthreads, GPGPU programming: CUDA
Numerical Methods
- Textbook: Linear Algebra by Strang
Main Topics: Advanced scientific computing
Operating Systems
- Textbook: Operating Systems by Arpaci-Dusseau
Main Topics: Processes and threads, synchronization, inter-process communication, memory management, file systems, scheduling, I/O, virtualization
C/C++ for Advanced Programmers
- Textbook: Standard for the Programming Language C++ by Standards Committee
Main Topics: Memory management, polymorphism, STL, template techniques, C++ idioms and libraries such as RAII, internationalization, multithreading, customizing I/O streams
Unix Systems Programming
- Textbook: Advanced Programming in the UNIX Environment by Stevens, Rago && Beginning Linux Programming by Matthew and Stones
Main Topics: RPC, IPC, threads, distributed programming, distributed objects, and operating systems
Advanced Computational Data Analysis
- Textbook: Mining of Massive Datasets by Rajaraman, Leskovec and Ullman
Main Topics: Generalized linear models, graphical models (Bayes nets), kernels and Support Vector Machines, and Markov models
Computational Data Analysis
- Textbook: Elements of Statistical Learning by Tibshirani, Data Mining: Concepts and Techniques by Han et al
Main Topics: Classification of data using techniques such as k-nearest neighbors, decision trees, naive Bayes, and support vector machines
Algorithms
- Textbook: Introduction to Algorithms by Cormen, Leiserson, Rivest and Stein (CLRS)
Main Topics: Sort/Search Algorithms, Divide & Conquer Techniques, Dynamic Programming, Data Structures, Graph Algorithms including Bellman-Ford, Dykstra, Prim and Kruskal
C Programming
- Textbook: C Programming Language by Kernighan, Ritchie (K&R) && Mastering Algorithms in C by Loudon
Main Topics: C memory management, control flow, and abstraction, basic and advanced data structures, rudiemntary algorithms, and API design
Databases
- Textbook: A First Course In Databases Systems by Ullman and Widom
Main Topics: relational algebra and calculus; subqueries; joins; database housekeeping (create table; insert into; delete; etc). How multiuser, distributed database systems work. Transaction commits; ACID; logs; locking; two-phase locking, integration of relational database management systems with application platforms and frameworks, database-back-ended web applications. Emerging directions a discussion on XML and its mapping to relational models, OLAP, semistructured data sets
Concepts Of Computer Science In Java
- Textbook: Building Java Programs by Reges and Stepp
Main Topics: foundational programming principles and practices for writing clean, readable code, and learning how think and solve problems like a computer scientist. Basic principles like procedural abstraction, recursion, and handling input and output, emphasis on theories and principles of Object Oriented software design, analyzing algorithms
Functional Analysis
- Textbook: Introduction to Real Analysis by Kolmogorov
Main Topics: Metric Spaces and Minkowski's Inequality, Continuous Mappings and Homeomorphisms, Contraction Mappings and the Fixed Point Theorem, Linear Spaces, Normed Linear Spaces and Banach Spaces, Inner Product and Hilbert Spaces, Continuous Linear Functionals, Linear Operators.
Measure Theory
- Textbook: Real Analysis by Royden
Main Topics:
Field Theory
- Textbook: Abstract Algebra by Dummit and Foote
Main Topics: Field Extentions, Galois Theory, Galois Groups.
Ring Theory
- Textbook: Abstract Algebra by Dummit and Foote
Main Topics:
Group Theory
- Textbook: Abstract Algebra by Dummit and Foote
Main Topics:
Mathematical Modeling
- Textbook: A Course In Mathematical Modeling by Mooney and Swift && Concepts of Mathematical Modeling by Meyer
Main Topics: Discrete logistic model and techniques used for analyzing nonlinear (dynamic) models: equilibrium states, stability test (using the first derivative), bifurcation values, periodic (cyclic) behavior, aperiodic (chaotic) behavior, cobweb diagrams.
Matrix models given by the so called Markov chains: transition matrices for which each column is a probabiliy vector (the sum of entries is 1). The dominant eigenvalue in this case is exactly 1 and the associated normalized eigenvector is again the steady-state probability vector. Perron-Frobenius Theorem: if the matrix A is regular (primitive), meaning a certain power of A has all entries positive, then there exists a simple positive eigenvalue of A that dominates (in absolute value) all the other eigenvalues. The dominant eigenvalue provides the overall growth rate of the model. It also has a corresponding eigenvector with all entries positive. Such an eigenvector (normalized so that the sum of entries is 1) provides the steady-state distribution of the matrix model: the long term proportion of the total population in each age class.
Linear Programming: geometric solution for two-variable case, simplex algorithm, duality.
Poincare-Bendixson Theorem. The general conclusion is that the asymptotic behavior of such systems (with continuous differentiable vector fields) is well understood both locally (near each steady-state) and globally: any bounded trajectory approaches either an equilibrium point, limit cycle or cyclic graph.
Local and global methods for analyzing non-linear autonomous systems. The local method is called linear analysis (linearization), while the global method has to do with nullcline analysis.
Higher dimensional (>2) nonlinear systems of differential equations for which complicated (chaotic) behavior is a real possibility. In particular, the Lorenz system exhibits random-like trajectories, and sensitive dependence to initial conditions.
Topology
- Textbook: Topology Without Tears by Morris
Main Topics:
Real Analysis II
- Textbook: An Introduction to Analysis by Kirkwood
Main Topics:
Real Analsysis I
- Textbook: An Introduction to Analysis by Kirkwood
Main Topics: Fields, order, completeness and the least upper bound axiom, interlude on cardinality, sequences in R, subsequences, Bolzano-Weierstrass, metric topology, continuous functions and their properties.
Advanced Linear Algebra
- Textbook: Linear Algebra by Friedberg, Insel and Spence
Main Topics:
Numerical Analysis II
- Textbook: Numerical Analysis by Sauer
Main Topics: Random Numbers and Applications, Trigonometric Interpolation and Fast Fourier Transform, Compression, Huffman Coding, Eigenvalues and Singular Value Decomposition, Applications of the SVD
Complex Analysis
- Textbook: Complex Variables by Fisher
Main Topics:
Linear Algebra
- Textbook: Linear Algebra by Nicholson
Main Topics:
Abstract Algebra II
- Textbook: A First Course in Abstract Algebra by Fraleigh
Main Topics:
Numerical Analysis I
- Textbook: Numerical Analysis by Sauer
Main Topics: Solving Equations, FPI, Newton's Method, Interpolation, Cubic Splines, Least Squares, Numerical Differentiation
Probability Theory & Statistics
- Textbook: Mathematical Statistics by Wackerly, Mendenhall and Scheaffer
Main Topics:
Abstract Algebra I
- Textbook: A First Course in Abstract Algebra by Fraleigh
Main Topics: