How to negate implications. Neha Nayak nayakne at stanford.edu 3. Welcome to CS103, an introduction to discrete mathematics, computability theory, and complexity theory! For quarterly enrollment dates, please refer to our graduate education section. Regular languages are closed under Universal turing machines, equivalence of 06/02. are equal or that a set is contained in another, If you have any questions in the meantime, feel free to email me at htiek@cs.stanford.edu with questions. The Foundations in Computer Science Graduate Certificate provides a solid course of study in the mathematical foundations of computing as well as important aspects of computer programming. And how can we reason about the answers to these questions with mathematical certainty? More undecidable problems. enumerable and recognizable languages, non-recognizable languages. 05/21. Stanford University. The course you have selected is not open for enrollment. Programming Abstractions (Stanford Course CS106B) or equivalent. 05/28. Learn the essential elements of computing theory including logic, proof techniques, combinatorics, algorithm analysis, discrete data models (sets, relations, trees), and finite automata Graphs: directed and undirected graphs, paths, connectivity and connected components, strong connectivity, 04/23. It's due next Friday at 2:30. It's due Friday at 2:30. 04/16. Learn how to model problems mathematically, reason about them abstractly and then apply techniques to explore their properties. union, intersection and complement, 05/09. 5/05 If you think the homeworks are too easy, Luca: Mondays and Wednesdays, 2:30-3:30pm, 474 Gates, Aditya Tuesdays and Thursdays, 10am-noon, Huang basement, Bryan Tuesdays and Thursdays, 2:30-4:30, Gates Basement, James Wednesdays 4-6pm, and Thursdays 5-7pm Meyer Library, 2nd floor, Neha Mondays 6-8pm, Huang Basement, and Fridays 9-11am, Huang basement. Aditya Tuesdays and Thursdays, 10am-noon, Huang basement … This course explores the answers to these questions and serves as an introduction to discrete mathematics, computability theory, and complexity theory. ©Copyright Solving the "fake coin" problem with the minimal number of measurements. 05/19. Proof that integers can always be written as a product of primes and of the "division algorithm" theorem, proofs by "infinite descent" using the well-ordering principle. Important Security Information: of regular expressions and DFAs and NFAs. Stanford, The halting problem is not decidable. not regular. topological sort if and only if it is acyclic, vertex-colorings of undirected graphs, I hope that you find these notes useful! Trevisan, Gates 474, Tel. and test regular expressions, Notes, sections 3.4.1 (can skip 3.4.1.1), 3.5.1, 3.5.3, 3.6.1, Notes, sections 5.1.1, 5.1.2, 5.2.1, 5.3 (skip starred sections), 5.4, Notes, sections 4.1, 4.2 (skip 4.2.2 and 4.2.3). 04/21. Aditya Palnikar aditpal at stanford.edu 4. Complexity theory, P and NP, part 2. Instructor: LucaTrevisan, Gates 474, Tel. Copyright Complaints   Trademark Notice. California P, NP, polynomial time reductions (not part of the syllabus for the final), 06/04. Since your browser does not support JavaScript, you must press the Continue button once to proceed. Introduction, summary of the content of the course, sets, Cantor's theorem, 04/02. Course availability will be considered finalized on the first day of open enrollment. Definition of Turing machines, variants of Turing machines. What are the theoretical limits of computing power? Mathematical Foundations of Computing Preliminary Course Notes Keith Schwarz Spring 2012 This is a work-in-progress draft of what I hope will become a full set of course notes for CS103. 05/14. Mathematics provides many powerful insights for current and future fundamental principles of computer science. More on minimizing the number of states of a DFA. We have an great quarter ahead of us filled with interesting and exciting results in the power and limits of computation, and I hope that you're able to join us. © Stanford University. Proofs by induction. Which ones cannot? Stanford, California 94305. Pigeonhole principle. Using the Myhill-Nerode theorem to prove that languages More on proofs by induction: strong induction, induction with several base cases, using a starting point different from zero. 04/18. Thank you for your interest. product of two odd integers is odd, how to argue that two sets This broad introduction to mathematical applications will prepare you to move forward and solve today’s most important problems within the computer science field. [lecture notes] [homeworks] [exams], Instructor: Luca Binary relations: partial orders, well-orderings, induction over well-orderings, equivalence relations, equivalence classes. Problem Set Eight goes out today. Problem Set Eight goes out today. Foundations in Computer Science Graduate Certificate, Stanford Center for Professional Development, Entrepreneurial Leadership Graduate Certificate, Energy Innovation and Emerging Technologies, Essentials for Business: Put theory into practice, Formal language theory such as finite automata, Turing machines and NP-completeness. James Shapiro jamess5 at stanford.edu Classesare MWF, 12:50-2:05, 420-040 Discussion sectionsare Tuesdays, 5:30-6:30pm in Thornton110 Office hours: 1. Use of this system is subject to Stanford University's rules and regulations. 05/16. 650 723-8879, email trevisan at stanford dot edu, Discussion sections are Tuesdays, 5:30-6:30pm in Thornton110, You can reach the whole CS103 staff at cs103-spr1314-staff@lists.stanford.edu, The final will be on June 6, 8:30-11:30am, in 420-40. Distinguishable and indistinguishable strings. The final exam is closed-book and closed-notes, but you can use two sheets of notes (each can be double-sided), Practice problems for the final and solutions, tool to construct Mapping reductions. See the Stanford Administrative Guide for more information. 04/04. epsilon-transitions. 04/14. Luca: Mondays and Wednesdays, 2:30-3:30pm, 474 Gates 2. [general info]  Definition of regular expressions. 05/12. Decidable and Undecidable problems, 05/30. Minimizing the number of states of a DFA. properties of boolean XOR, one-time pad. The handout on the Honor Code talks about how the Stanford Honor Code applies to CS103 - you are expected to read this handout and abide by its terms throughout the quarter. See you soon! "Just do it" proofs: sum of two odd integers is even, Proving properties of graphs: topological sort, a directed graph has a In the course of working through it, you'll get some experience designing context-free grammars, playing around with connections between different classes of languages, building Turing machines, and setting a firm foundation for exploring the limits of computing. Introduction, summary of the course, Cantor's theorem, 05/21. Right now, the notes only cover up through the end of the first week. Logging in lets you access other protected Stanford websites with this browser, not just the website you requested. Bryan Hooi bhooi at stanford.edu 2. If you have any comments, criticisms, or suggestions, please email me at htiek@cs.stanford.edu. For the first part of the course, on sets, graphs, and proofs: For the rest of the course, on automata, computability and complexity: 03/31. In the course of working through it, you'll get some experience designing context-free grammars, playing around with connections between different classes of languages, building Turing machines, and setting a firm foundation for exploring the limits of computing. Mathematics provides many powerful insights for current and future fundamental principles of computer science. The course schedule is displayed for planning purposes – courses can be modified, changed, or cancelled. Formal definition of DFA, introduction to NFA, examples of NFA, converting an NFA to DFA, 05/07. Proofs by contrapositive and contradiction. What problems can be solved with computers? Learn how to model problems mathematically, reason about them abstractly and then apply techniques to explore their properties. Please click the button below to receive an email when the course becomes available again. 650 723-8879, email trevisan at stanford dot edu TAs: 1. Preview of proofs of contradiction: square root of 2 is not rational. Equivalence NP-completeness of SAT (not part of the syllabus for the final), 03/31. 05/23. The syllabus for the final is up to the 5/28 lecture. The Myhill-Nerode theorem. 94305. This broad introduction to mathematical applications will prepare you to move forward and solve today’s most important problems within the computer science field. an undirected graph has a two-coloring if and only if it has no odd cycle, 05/05. A formula for the sum of squares. There are infinitely many primes.

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