CSE 581: Theory

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CSE 581: Theory

Classes
Asynchronous online via Google Drive (Discrete Mathematics and Theory of Computation) using @stonybrook.edu email account.
Instructor
Prof. Pramod Ganapathi
Office hours: Mo 09:00-12:00 PM via Zoom
Note
This course is mainly for satisfying the prerequisites of algorithms and data structures. It will NOT count as a lecture course for CS M.S. students. It will NOT count towards CS Ph.D. quals. However, its credits will count for graduation for both CS M.S. and CS Ph.D.

Course Description
The course consists of two parts. The first part covers the part of mathematics that is extensively used in computer science. The topics covered include: logic (propositional logic and predicate logic), number theory, proof techniques, sequences, recursion, functions, relations, and sets. The second part covers the mathematical theory of computation, computers, algorithms, and complexity. The topics covered include: computation models, grammars accepted by different computation models, languages accepted by different computation models, Turing-complete systems, algorithmically unsolvable problems, and algorithmically hard problems.
Prerequisites
Programming experience in at least one high-level programming language and competence in using programming tool chains (writing, compiling, running and debugging programs). There is no coding in this course, however, the knowledge of programming languages tremendously helps to understand the theoretical topics.
Credits
3
Course Outcome
At the end of the course, the students should have the following knowledge, skills, and wisdom:
  • An ability to verify if a mathematical argument is valid (i.e., logical) and sound (i.e., truthful)
  • An ability to verify the correctness of proofs of some existing theorems and prove some new theorems
  • An ability to use mathematical concepts such as sequences, functions, relations, and sets in computing
  • Understand the motivations behind and differences between various computation models
  • An ability to determine the algorithmic complexity or algorithmic impossibility of a given computational problem
  • An ability to determine the simplest computation model to solve a given computational problem
Textbooks
  • [DM] Discrete Mathematics: Introduction to Mathematical Reasoning. Susanna S. Epp. Brief Edition.
  • [R] Automata, Computability and Complexity: Theory and Applications. Elaine Rich.
  • [LP] Elements of the Theory of Computation. Harry R. Lewis and Christos H. Papadimitriou. 2nd Edition.
  • [M] Introduction to Languages and the Theory of Computation. John Martin. 4th Edition.
Grading
Course requirements and grading are as follows:
  • Homework: 40%
  • Midterm: 30%
  • Final: 30%
Homework
Homework will be posted on Brightspace. Homework must be written on plain sheets of paper, scanned using a good scan app, and a single scanned PDF must be submitted on Brightspace. The PDF must have the student ID as the file name. Late submissions will not be graded for any reason (including oversleeping, forgetting, PC issues, technical issues, Brightspace issues, traveling, etc), except in the case of medical emergencies (with documentation submitted to and verified by the Student Support Team) and on the discretion of the instructor based on a case-by-case basis. It is strongly recommended to submit at least one version three days before the deadline. A student can submit an infinite number of versions of the answer sheets PDF to the Brightspace. We only evaluate the last/final version of the solutions PDF uploaded on Brightspace before the deadline.
Students should not submit the first version of their homework at the exact deadline or later or a few seconds/minutes just before the deadline. Because, we do not consider the time at which a homework was submitted, we consider the time at which the homework was successfully up on Brightspace (with all pages in human-readable form) and it takes a few seconds/minutes to upload on Brightspace. If Brightspace flags the homework as late, it is late.
Regrade requests deadline is 1 week after getting the homework/exam results on Brightspace.
Makeup Exams
Makeup exams will not be given for any reason (including oversleeping, forgetting, PC issues, technical issues, Brightspace issues, traveling, etc), except in the cases of medical emergencies (with documentation submitted to and verified by the Student Support Team) and on the discretion of the instructor based on a case-by-case basis; student participation in university sponsored events (with documentation); and religious absences (with documentation).
Attendance
Students are expected to attend every class, report for examinations and submit major graded coursework as scheduled. If a student is unable to attend lecture(s), report for any exams or complete major graded coursework as scheduled due to extenuating circumstances, the student must contact the instructor as soon as possible. Students may be requested to provide documentation to support their absence and/or may be referred to the Student Support Team for assistance. Students will be provided reasonable accommodations for missed exams, assignments or projects due to significant illness, tragedy or other personal emergencies. In the instance of missed lectures or recitations, the student is responsible for reviewing posted slides, reviewing recorded lectures, seeking notes from a classmate, etc. Please note, all students must follow Stony Brook, local, state and Centers for Disease Control and Prevention (CDC) guidelines to reduce the risk of transmission of COVID. For questions or more information click here.
Additional Resources
  • Books -- Discrete Mathematics
    • [SWDM] A Spiral Workbook for Discrete Mathematics. Harris Kwong.
    • [MCS] Mathematics for Computer Science. Eric Lehman, F. Thomson Leighton, and Albert R. Mayer.
    • [BP] Book of Proof. Richard Hammack.
    • [DMOI] Discrete Mathematics: An Open Introduction. Oscar Levin. 3rd Edition.
    • [DFC] Delftse Foundations of Computation. Stefan Hugtenburg and Neil Yorke-Smith.
    • [ENT] Elementary Number Theory. W. Edwin Clark.
    • [ADS] Applied Discrete Structures. Alan Doerr and Kenneth Levasseur.
    • [FOCS] Foundations of Computer Science. Alfred V. Aho and Jeffrey D. Ullman.
  • Books -- Theory of Computation
    • Margaret Fleck and Sariel Har-Peled's Notes.
    • Johan Hastad's Notes.
    • Jeff Erickson's Notes.
    • Michael Levet's Notes.
    • Jim Hefferson's Notes.
    • Peter Gacs and Laszlo Lovasz's Notes.
    • [S] Introduction to the Theory of Computation. Michael Sipser. 3rd Edition.
    • [K] Automata and Computability. Dexter C. Kozen.
    • [HMU] Introduction to Automata Theory, Languages, and Computation. John E. Hopcroft, Rajeev Motwani, and Jeffrey D. Ullman. 2nd Edition.
    • [MS] Introduction to Theory of Computation. Anil Maheshwari and Michiel Smid.
    • [FB] The Language of Machines. Robert W. Floyd and Richard Biegel.
    • [DK] Problem Solving in Automata, Languages, and Complexity. Ding-Zhu Du and Ker-I Ko.
    • Turing's Vision. Chris Bernhardt.
    • The Annotated Turing. Charles Petzold.
    • The Outer Limits of Reason. Noson S. Yanofsky.
  • Video Courses
    • Portland State University. Harry Potter.
    • IIT Kanpur. Raghunath Tewari.
    • ADUni. Shai Simonson.
  • JFLAP Software
    • Education tool to help experiment with DFA, regular expressions, NFA, grammars, and Turing machines.
    • Download.
    • Tutorial videos.
    • Book.
  • LaTeX
    • [OL] Learn LaTeX in 30 Minutes. Overleaf.
    • [WBL] Wikibook on LaTeX. Wikipeople.
    • [NSIL] The Not So Short Introduction to LaTeX. Tobias Oetiker.
    • [LCN] LaTeX for Complete Novices. Nicola L. C. Talbot (More Books).
    • [MML] More Math into LaTeX. George Gratzer. 4th Edition.
    • [LT] LATEX Tutorials. Indian Users Group.
    • [SIL] A Simplified Introduction to LaTeX. Harvey J. Greenberg.
    • More Books
  • Mathematical Writing
    • [SMW] Mathematical Writing. Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts.
    • [HWMS] Handbook of Writing for the Mathematical Sciences. 2nd Edition. Nicholas J. Higham.

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