Algebraic and Numerical Algorithms Course ID 15795 Description This course will provide some implementation motivated perspectives on algebraic and numerical algorithms, and will somewhat follow the Complexity and Linear Algebra semester program at the Simons Institute (https://simons.berkeley.edu/programs/complexity-linear-algebra). It will normally meet on Wednesdays and Fridays, with some Monday meetings to fit the schedule of the program. Key Topics Topics covered include polynomials, bit complexity, and numerical approximation/perturbation schemes. Required Background Knowledge Strong mathematical skills, familiarity with fundamental algorithms, good implementation skills. Presentation will assume some proficiency with algebra, number theory, and problem solving. An ideal background is mastery of either: Putnam A1~A3/B1~B3 (minus geometry); or IMO Shortlist C1~C4/N1~N2/A1~A2; or AtCoder ~1000-rated problems (minus data structures). Course Relevance All levels - Please refer to Required Background Knowledge (Prerequisite Knowledge). Undergraduate students should register for 15-495. Course Goals Familiarity with key tools in the design and analysis of algebraic and numerical algorithms. Including the use of polynomials / field extensions, and ways to analyze and control precision. Learning Resources Online paper repositories such as arXiv, as well as online autograders. Assessment Structure 60% homework, 10% participation, 30% project. Homework consist of submissions to problem sets, projects can be either presentations or UCup/AtCoder results. Extra Time Commitment UCup/AtCoder are on Saturdays, but are optional
