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Appl Mod Algebra

by: Mrs. Preston Lehner

Appl Mod Algebra MATH 312

Mrs. Preston Lehner
GPA 3.87


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This 2 page Class Notes was uploaded by Mrs. Preston Lehner on Thursday October 29, 2015. The Class Notes belongs to MATH 312 at University of Michigan taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/231508/math-312-university-of-michigan in Mathematics (M) at University of Michigan.

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Date Created: 10/29/15
Course Goals and Policies University of Michigan Math 416 Fall 2004 Theory of Algorithms September 13 2004 1 Infomation Title Math 416 Theory of Algorithms Time Place 1068 East Hall Prerequisites Math 312 or 412 or EECS 203 and EECS 281 or permission Text Introduction to Algorithms 2e Cormen Leiserson Rivest and Stein httpmitpressmit edualgorithms Follow links for errata Webpage http http www cse umich edu mart inj smath416 Instructor Martin Strauss Of ce central campus 3063 East Hall MWF Of ce north campus 2238 EECS Tues amp Thurs Email mart inj s umich edu Of ce hours TBA and by appointment Students with disabilities should obtain a Veri ed Individualized Services and Accommodations VISA form and will be accommodated according to university policy ee http www umich edu sswdindex html 2 Goals We will learn techniques for analysis of algorithms This includes language for discussing algorithms sepa rately from their implementation and particular inputs Is the algorithm correct on all or most inputs Is it approximately correct Is the algorithm ef cient in terms of run time memory space or other resource Is it ef cient on all or most inputs If the algorithm behaves randomly often a good thingl is the algorithm correct or ef cient for most of its randomly chosen runs Will the algorithm be run once or run many times In the latter case do we know in advance the sequence of inputs After developing the appropriate vocabulary we study tools for answering these questions with the rigor of mathematical proof The answer may be negativeithere is no algorithm that ef ciently solves our problem We also design simple algorithms and perform simple modi cations to existing algorithms Typically the analysis is dif cult enough even if the algorithms are simplel As a secondary goal to illustrate our techniques we will study particular algorithms that are fundamental andor of particular interest to the students These might include sorting matrix multiplication Fast Fourier Transform and primality testing There will be no programming assignments 3 Required Work There will be homework assignments two midterms and a nal Unless speci ed otherwise all work is expected to be completed individually With proper citation students may use books and static internet pages excluding for example mail to a human expert i en group work is allowed each student participating in group must have full understanding of all the work submitted by the group Each student must submit hisher own paper and indicate other members of the group Group members must be other students currently registered for this class The nal will count for 40 of the grade Each of the midterms and the combined homeworks will each count 20 of the grade You will be responsible for reading electronic announcements which will be posted on a web page andor sent by emaili Please advise me as soon as possible about any unusual bureaucratic circumstances eg expected ab sences from exams special requirements as to grades etc 4 Course Outline 0 Basics7nonRandomized 7 CLRS 172 Appendix A CLRS 374i Preliminaries asymptotic growth recursive algorithms 7 Additional notes generating functions sums of binomial symbols 7 CLRS 61764 Heapsort algorithm data structures loop invariants o Basics7Probability 7 CLRS 5 Appendix Cil C2 C3 C5 7 Additional notes median of means CauchySchwarz inequality 7 CLRS 7 9 More sorting and selection algorithms randomized algorithms average case analysis 7 CLRS 81 lower bound 7 CLRS11i111i211i311i5 Hashing 7 Additional notes random variables of limited independence 0 MIDTERMI o Metaalgorithmic techniques 7 CLRS 152 153 Matrixchain multiplication algorithms dynamic programming 7 CLRS 162 163 Huffman code construction algorithm Greedy Algorithms o Amortized analysis 7 CLRS 1717173 0 Math problems 7 CLRS 28 Matrices 7 CLRS 2917292 Linear Programming 7 CLRS 3017302 FFT 7 CLRS 31 Number theory modular arithmetic primality testing RSA cryptosystem o MIDTERM H o NPCompleteness


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