MATH 490

Spring 2021 Part of Term 1

Part of Term 1
Jan 25-May 5

Advanced Topics in Mathematics

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Credit: 1 TO 4 hours.

Deals with selected topics and applications of mathematics; see Class Schedule or department office for current topics.

1 to 4 undergraduate hours. 1 to 4 graduate hours. May be repeated with approval. Prerequisite: Consent of instructor.

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MATH 490 class schedule data for spring 2021
CRN	Type	Section	Time	Day	Location	Instructor	Section Details
47123	Online	AH	11:00AM -11:50AM	MWF	n.a.	Hirani, A	Part of Term: 1 Date Range: 01/25/21-05/05/21 Credit: 3 hours Section Title: Computational Math Section Info: Computational Math. Prerequisites: Successful completion of CS 101 or 125 or prior programming experience in Python, C, C++ or Java; as well as successful completion of Math 347 (or CS 173). This is a project-based course that will guide students through a computational way of approaching problems. Topics covered will include network and graph algorithms, topological data analysis, computer algebra and cryptography algorithms. Programming will be done in Python and its extension that the SageMath environment provides. The format will be short lectures and short programming exercises twice a week with longer project work day once a week. In addition students will select a longer final project and do an in-class presentation in the last week or so of class. The 4 main goals of this course are: (1) Improve programming skill and algorithmic thinking; (2) Prepare for industrial computational math work; (3) Prepare for future math courses by learning to use computation to play with examples; (4) Prepare for research in mathematics using a computer as a tool.
49529	Online	EK	10:00AM -10:50AM	MWF	n.a.	Kirr, E	Part of Term: 1 Date Range: 01/25/21-05/05/21 Credit: 3 hours Section Title: Topological Degree Theory Section Info: Topological Degree Theory. Prerequisite: Math 241 and Math 347 and familiarity with the algebraic manipulation of complex numbers. Description: Why can’t you comb your hair without getting a cowlick? Can you perfectly halve three slices (say two of bread and one of ham) which might be unequal and imperfectly stacked, by a single sharp knife cut? The answers to both questions are given by some very rigid objects called topological invariants which are studied in algebraic and differential topology. For more details please see https://go.math.illinois.edu/SP21EK . The course grade will be based on homework, two midterms, and a final project. Restriction(s): Not intended for First Time Freshman students.
70047	Online	QC	12:00PM -12:50PM	MWF	n.a.	Junge, M	Part of Term: 1 Date Range: 01/25/21-05/05/21 Credit: 3 hours Section Title: Quantum Computing Section Info: Quantum Computing. Prerequisites: Linear algebra is a minimal requirement, and some exposure to quantum mechanics is recommended, for example through classes in physics or IGL. Alternatively, students with a background in quantum computing will satisfy the prerequisites. Introduction to basic quantum mechanics and information theory. This will be combined in discussing mathematical tools relevant for quantum information theory. For further information see Math 595 MJ at https://math.illinois.edu/timetable