Coursework

Multivariable calculus covering parameterized curves, partial derivatives, multiple integrals, and vector calculus. Provides the optimization geometry underlying numerical methods and machine learning.

Vector spaces, linear transformations, eigenvalues, and standard matrix factorizations with rigorous proof writing. Core mathematical language for data systems, machine learning, and graphics.

Logic, sets, recursion, graph theory, and asymptotic analysis with a focus on discrete structures. Direct foundation for algorithm design and database query reasoning.

Probability axioms, discrete and continuous distributions, expectation, moment generating functions, conditional probability, multivariate distributions, and the central limit theorem.

Transistor-level logic, combinational and sequential circuit design, and introductory assembly programming. Establishes the hardware substrate that systems software runs on.

C programming, virtual memory, the memory hierarchy, caching, assembly, and linkers. Essential low-level knowledge directly applicable to database storage engines and OS internals.

Scheduling, virtual memory, file systems, synchronization, and I/O handling through xv6 implementation. Covers the core abstractions that operating systems provide to user-space programs.

Protocol layering, reliable transmission, congestion control, routing, and widely deployed protocols including TCP/IP and HTTP. Foundation for understanding communication in distributed systems.

Relational algebra, B-tree indexing, buffer pool management, query processing, concurrency control, and recovery. Covers both the theory and the engineering decisions behind real database systems.

Distributed storage and computation using Spark, Kafka, and HDFS with Python. Connects database internals knowledge to production-scale analytical workload patterns.

Algorithm design paradigms including greedy, divide-and-conquer, dynamic programming, and reductions to NP-completeness. Provides the analytical framework for evaluating query plan complexity.

Search, knowledge representation, probabilistic reasoning, and machine learning fundamentals. Broadens perspective on data-driven approaches alongside systems-focused coursework.

Object-oriented design, linked data structures, abstract data types, and introductory complexity analysis in Java. Builds the programming foundations required for advanced systems coursework.

Balanced search trees, graphs, hash tables, and complexity analysis in professional-grade Java. Bridges foundational data structures with performance-critical production implementations.

Data management, probability distributions, statistical inference, and simple linear regression using R.

Practical R programming for data manipulation, exploratory analysis, and visualization.