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         Pipelining Computer Science:     more books (15)
  1. Design considerations for parallel graphics libraries (SuDoc NAS 1.26:194935) by Thomas W. Crockett, 1994

21. Computer Science 294-7, Lecture #2
computer science 2947 lecture 2 Computing Requirements for Reconfigurable Computing Such pipelining doesn t help latency, but will help bandwidth.
http://www.cs.caltech.edu/~andre/courses/CS294S97/notes/day2/day2.html
Computer Science 294-7 lecture #2
Computing Requirements for Reconfigurable Computing
VLSI Scaling
Notes by Nick Weaver Administrivia: The Course Calendar is online, and contains items including handouts, slides, lecture notes (like these), reading lists and supplemental reading, and other important information. It will be continually updated during the course of the class. Today's topics: Computing requirements for reconfigurable devices and VLSI scaling. These notes generally follow the slides, and the numbers refer to the order in the handed out slides.
Slide 2: The first slide was a discussion point for the different elements and what needs to be configured in order to program the device.
Slide 3: These are two sample programmable devices, a large block of memory or combinational logic. The problems are potential inefficiencies, the exponential size in the memory, feedback and routing issues, and, most importantly, NO STATE! This slide was designed as a discussion point. Without state, there are limits on reuse of components, and, if an infinite input stream is required, the lack of state implies an infinite number of these devices are required.
Slide 4: We need registers for pipelining (for performance), to communicate data between cycles (eg in an FSM or some feedback loop). The general buzzword used for both these uses is

22. Computer Science 294-7, Lecture #5
computer science 2947 Lecture 5 Instructions. Notes by Amit Mehrotra the structure of the problem and heavy pipelining to achieve the fastest speed.
http://www.cs.caltech.edu/~andre/courses/CS294S97/notes/day5/day5.html
Computer Science 294-7 Lecture #5
Instructions
Notes by Amit Mehrotra
Slide 3: An overview of the Programmable Active Memory (PAM) as detailed in Programmable Active Memories: Reconfigurable Systems Come to Age . The core consists of a 4x4 array of FPGA's (XC3090) with 4 1Mb RAM for locale memory. The maximum memory bandwidth is 400 MB/s. It also has four 32b external connectors three of which are of 400 MB/s capacity. The fourth connector links to the host interface through input and output FIFO's. The clock on the board is tunable to allow different length critical paths. Also the clock can be dynamically tuned for a slow and infrequent operation.
Slide 4: The authors claim the synthesis tools were too wasteful for area and performance, and in an FPGA environment which already suffers from performance penalty aver raw silicon implementation. Schematic capture is very laborious to be viable. So a netlist generator has been developed which gives an algorithmic description of the structure. The language used for "hardware description" is C++.
Slide 5: This slide illustrates an example of a netlist generator which generates an adder. Also, logic operators can be easily annotated with placement directives. This information is optional. However, the tool performs best when regular blocks like datapaths are placed relative to each other and automatic placement is performed for the control logic.

23. Computer Science @ UC Davis | Course Descriptions
s Introduction to RISCphilosophy, and interactions with pipelining, orthogonal instruction sets,......computer science Home » Courses » Course
http://www.cs.ucdavis.edu/courses/exp_course_desc/154B.html
@import url("../../css/csstyle.css"); Home Courses Course Descriptions
ECS 154B COMPUTER ARCHITECTURE (4) I, II, III
Lecture: 3 hours Discussion: 1 hour Prerequisites: Course ECS 154A or EEC 170, and course ECS 110 Grading: Letter; two midterms (20% each), final exam (40%) and programming and digital design work (20%) Catalog Description:
Hardwired and microprogrammed CPU design. Memory hierarchies. Uniprocessor performance analysis under varying program mixes. Introduction to pipelining and multiprocessors. Expanded Course Description:
  • Hardwired and Microprogrammed CPU Design
    Internal bus systems. Register transfer languages. Microprogramming. Homework using digital design software to implement part or all of a simple CPU. Memory Hierarchies
    General idea of multilevel memory systems. Emphasis here is on caches, since virtual memory is covered in courses 154A, 150, 151AB. Uniprocessor Performance Analysis
    Instruction set profile analyses under varying program mixes. Cost/performance tradeoffs. Introduction to RISC philosophy, and interactions with pipelining, orthogonal instruction sets, etc. Multiprocessor Speedup
    Introduction to shared-memory and message-passing multiprocessor systems.
  • 24. Computer Science @ UC Davis | Course Descriptions
    s Overview of pipelining;Advanced pipelining topics; Fine grain (Instruction level) Parallelism......computer science Home » Courses » Course
    http://www.cs.ucdavis.edu/courses/exp_course_desc/201A.html
    @import url("../../css/csstyle.css"); Home Courses Course Descriptions
    ECS 201A ADVANCED COMPUTER ARCHITECTURE (4) I
    Lecture: 3 hours Termpaper: 1 hour Prerequisite: Course ECS 154B or EEC 170; course ECS 150 Grading: Letter; homework (30%), exam (30%), research project (40%) Catalog Description:
    Modern research topics and methods in computer architecture. Design implications of memory latency and bandwidth limitations. Performance enhancement via within-processor and between-processor parallelism. Term project involving student-proposed extensions/modifications of work in the research literature. Not open for credit to students who have completed course 250A. Goals:
    To provide the student with an overview of the current state of modern computer architecture, and to prepare the student for the rest of the advanced computer architecture sequence. Expanded Course Description:
  • Fundamentals of Computer Design
  • Overview of history and trends in Processor design Measuring and Reporting Performance Motivations for the modern trend towards simpler architectures Performance Enhancement Techniques
  • Overview of Pipelining Advanced Pipelining topics Fine grain (Instruction level) Parallelism Memory System Issues
  • Discrepancies between memory speed and processor speed Introduction to multiple cache systems Overview of Advanced Storage systems Parallel Processing
  • Fine-and coarse-grained parallelism Introduction to tightly-and loosely-coupled designs
  • 25. Computer Laboratory - Computer Science Tripos Syllabus - Computer Design
    computer Laboratory computer science Tripos Syllabus computer Design An algorithmic viewpoint. Basic processor hardware. pipelining and data paths.
    http://www.cl.cam.ac.uk/DeptInfo/CST/node30.html
    Computer Laboratory
    Computer Science Tripos Syllabus - Computer Design Computer Laboratory Computer Science Tripos Syllabus - Computer Design
    Next: Concurrent Systems and Applications Up: Michaelmas Term 2004: Part Previous: Michaelmas Term 2004: Part Contents

    Computer Design
    Lecturer: Dr S.W. Moore No. of lectures: Prerequisite courses: none, but Operating Sustems would be helpful This course is a prerequisite for Comparative Architectures (Part II) and VLSI Design (Part II).
    Aims
    The aims of this course are to introduce the hardware/software interface models and the hardware structures used in designing computers. The first eight lectures are concerned with the hardware/software interface and cover the programmer's model of the computer. The last eight lectures look at hardware implementation issues at a register transfer level.
    Lectures
    • Introduction to the course and some background history. Historic machines. EDSAC versus Manchester Mark I. Introduction to RISC processor design and the ARM instruction set. ARM tools and code examples.

    26. Computer Laboratory - Diploma In Computer Science Syllabus - Computer Design
    computer Laboratory Diploma in computer science Syllabus computer Design Basic processor hardware. pipelining and data paths.
    http://www.cl.cam.ac.uk/DeptInfo/Diploma/node9.html
    Computer Laboratory
    Diploma in Computer Science Syllabus - Computer Design Computer Laboratory Diploma in Computer Science Syllabus - Computer Design
    Next: Continuous Mathematics Up: Michaelmas Term 2004 Previous: Java and the Unix Contents

    Computer Design
    Lecturer: Dr S.W. Moore No. of lectures:
    Aims
    The aims of this course are to introduce the hardware/software interface models and the hardware structures used in designing computers. The first eight lectures are concerned with the hardware/software interface and cover the programmer's model of the computer. The last eight lectures look at hardware implementation issues at a register transfer level.
    Lectures
    • Introduction to the course and some background history. Historic machines. EDSAC versus Manchester Mark I. Introduction to RISC processor design and the ARM instruction set. ARM tools and code examples. Operating system support including memory hierarchy and management. Intel x86 instruction set. Java Virtual Machine. Executing instructions. An algorithmic viewpoint. Basic processor hardware. Pipelining and data paths.

    27. MIT OpenCourseWare | Electrical Engineering And Computer Science | 6.823 Compute
    MIT OpenCourseWare » Electrical Engineering and computer science 11,Complex pipelining (PDF). 12, Out of Order Execution Register Renaming (PDF)
    http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-823Compu
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    • Course Home Syllabus Calendar ... Computer System Architecture, Spring 2002
      Lecture Notes
      LEC # TOPICS History of Calculation and Computer Architecture ( PDF Influence of Technology and Software on Instruction Sets: Up to the Dawn of IBM 360 ( PDF Complex Instruction Set Evolution in the Sixties: Stack and GPR Architectures ( PDF Micro-Programming ( PDF Simple Instruction Pipelining PDF Pipeline Hazards ( PDF Multilevel Memories ( PDF Cache (Memory) Performance Optimization ( PDF Virtual Memory Basics ( PDF Virtual Memory: Part Deux ( PDF Complex Pipelining ( PDF PDF PDF Advanced Superscalar Architectures ( PDF VLIW/EPIC: Statically Scheduled ILP ( PDF Vector Computers ( PDF Symmetric Multiprocessors: Synchronization and Sequential Consistency ( PDF Cache Coherence ( PDF Relaxed Memory Models ( PDF Microprocessor Evolution: 4004 to Pentium Pro ( PDF Advanced CISC Implementations: Pentium 4 ( PDF Virtual Machines and Dynamic Translation: Implementing ISAs in Software ( PDF Multithreaded Processors ( PDF Embedded Computing ( PDF Parallel Processors ( PDF

    28. UMASS Boston Department Of Computer Science
    University of Massachusetts, Boston computer science Colloquium. Monday, 12 March2001, 230 PM S/2/063. pipelining LU Decomposition
    http://www.cs.umb.edu/News_Events/Lectures_Seminars/Colloquiums/talk03-12-01.htm
    Colloquiums/Seminars University of Massachusetts, Boston
    Computer Science Colloquium Monday, 12 March 2001, 2:30 PM
    S/2/063 Pipelining LU Decomposition:
    Automatically Transforming Loop Computations for
    Distributed-Memory Machines Carl D. Offner
    Gem Compiler Group, Compaq Computer Corporation
    There are two big issues that a compiler encounters when generating code for a distributed-memory machine (or more generally, for a multi-processor machine with non-uniform memory access):
    1. Distribute data over the memories of the machine, and distribute computations over the processors of the machine in such a way that the processor executing a particular computation is near the memory holding the data it accesses.
    2. Schedule the execution of computations with respect to each other for maximum parallelism while respecting the semantics of the original program.
    One way of dealing with the first problem is to have the programmer specify an appropriate mapping of data to memories. Given this mapping, the compiler can generally do a pretty good job of mapping computations to processors so that as many computations as possible use only local, as opposed to remote, memory references.

    29. CS 654: Computer Architecture
    computer science 654 (fall 2003) Olsson 011, TTh 930-1045 am Th, 9/11,pipelining wrap up basic material, consider pipeline complications
    http://www.cs.virginia.edu/~skadron/cs654/
    Computer Science 654
    (fall 2003)
    Olsson 011, T-Th 9:30-10:45 am
    Computer Architecture
    Instructor
    Kevin Skadron
    Office: 215 Olsson Hall
    Office hours: after class or by appt.
    Phone: x2-2042
    skadron@cs
    TAs
    Qiuhua Cao
    Office: 235 Olsson Hall
    Office hours: M-W 7:00-7:45pm or by appt.
    qc9b@cs Weisheng Si
    Office: 237 Olsson Hall Office hours: Tu-Th 4:00-4:45pm or by appt. ws4u@cs
    Announcements
    Assignments
    (Unless noted otherwise, written assignments should be turned in as hardcopy to the CS654 folder in Olsson 204; programming assignments should be submitted by e-mail to cs654@cs with a pointer to the directory containing all relevant files)
    • due Wednesday, 9/3 at 9:30 am ( PDF Second programming exercise (pipelining phase one) another extension due to the hurricane! due Monday, 9/22, at 9:30 am

    30. COMPUTER SCIENCE TECHNICAL REPORT ABSTRACTS
    School of computer science, Carnegie Mellon University pipelining is a widelyused technique that query execution engines employ to improve individual
    http://reports-archive.adm.cs.cmu.edu/anon/2005/abstracts/05-122.html
    CMU-CS-05-122
    Computer Science Department
    School of Computer Science, Carnegie Mellon University
    CMU-CS-05-125 Deadlock Resolution in Pipelined Query Graphs Vladislav Shkapenyuk, Ryan Williams,
    Stavros Harizopoulos, Anatassia Ailamaki March 2005 CMU-CS-05-122.ps
    CMU-CS-05-122.pdf

    Keywords: Pipelining, deadlock resolution, dynamic buffer management, query plan, materialization
    Pipelining is a widely used technique that query execution engines employ to improve individual query execution times. In recently proposed settings, pipelining is used as an alternative to materialization to evaluate query plan graphs , where nodes in a query plan can have multiple parents. Such scenarios include shared table scans, runtime operator sharing, parallel sorting, and pipelined Multi-Query Optimization (MQO) plans. While pipelining in query graphs can increase performance, it can also lead to runtime deadlocks. The existing deadlock solutions focus on total deadlock prevention by statically deciding between pipelining and materialization, and apply only to MQO. The lack of runtime information leads to highly conservative decisions. Formally, this conservatism makes it NP-hard to find an optimal pipelining strategy that materializes a minimum cost set of nodes in a query graph. We propose a novel dynamic scheme for detecting and resolving deadlocks in pipelined query graphs. Instead of statically determining what nodes to materialize, we pipeline every pipelinable operator in the query plan, resolving deadlock when it arises by materialization. At runtime, more information about producerconsumer behavior is available and as a result, the problem of detecting and resolving deadlock becomes polynomial time solvable, where each particular deadlock resolution is of minimum cost. Our techniques are applicable to any system that uses pipelined query graphs. An evaluation on TPC-H and Wisconsin benchmarks demonstrates cases where our approach eliminates all unnecessary materializations, and minimizes the overall query execution cost.

    31. COMPUTER SCIENCE TECHNICAL REPORT ABSTRACTS
    School of computer science, Carnegie Mellon University pipelining has beenused previously, but the method used here allows for asynchronous execution
    http://reports-archive.adm.cs.cmu.edu/anon/1998/abstracts/98-127.html
    CMU-CS-98-127
    Computer Science Department
    School of Computer Science, Carnegie Mellon University
    CMU-CS-98-127 Experiments with Parallel Pointer-Based Algorithms Margaret Reid-Miller May 1998 Ph.D. Thesis Unavailable Electronically
    Keywords: PRAM, algorithms, list ranking, dictionaries, balanced trees, treaps, pipelining, set operations, pointer-based implementation
    The algorithms as implemented, however, do not have optimal depth (parallel time). This dissertation shows how to reduce the depth of the tree algorithms to make them optimal by using pipelining. Pipelining has been used previously, but the method used here allows for asynchronous execution and for pipeline delays that are data dependent and dynamic. Rather than making the coding more difficult, the method lets the user write the algorithms using futures (a parallel language construct) and leaves the management of the pipelining to an efficient runtime system. To determine the runtime of algorithms, I first analyze the algorithms in a language-based cost model in terms of work and depth of the computations, and then show universal bounds for implementing the language on various machines. 100 pages Return to: SCS Technical Report Collection
    School of Computer Science
    homepage
    This page maintained by reports@cs.cmu.edu

    32. Carleton College: Computer Science: Course Information
    Prerequisite computer science 117 or consent of the instructor. assemblylanguages, memory hierarchies, caches, RISC architectures and pipelining.
    http://apps.carleton.edu/curricular/cs/courses/
    Skip Navigation Text Only/ Printer-Friendly Site Navigation Information for... - Prospective Students - Current Students - International Students - Alumni - Visitors Quick Links: - A to Z Guide - Academic Departments - Admissions - Athletics - Campus Offices - Carleton News - Employment Opportunities - Event Calendars - Giving to Carleton - Gould Library - Phone/Email Directory - Registrar's Office - Site Map - The Arts at Carleton You are here: Academic Departments Math/CS Computer Science
    Computer Science ...
    • Overview Courses The Major Resources Events Newsletter ... Printer-Friendly
      Course Information
      • 2005-2006 Courses: Browse by Course Number Browse by Term
        CS 107: Explorations in Computer Science
        This course is designed for students who have never taken a computer science course. It provides an overview of computer technology and an introduction to the fundamental concepts and applications of computer science. We will explore both the technical aspects and the social, political, and ethical aspects of computers and computer technology. Students who have taken Computer Science 127 may not enroll in Computer Science 107. 6; Mathematics and Natural Sciences; offered

    33. Carleton College: Computer Science: Course Information
    Students who have taken computer science 127 may not enroll in computer science107. memory hierarchies, caches, RISC architectures and pipelining.
    http://apps.carleton.edu/curricular/cs/courses/?order_courses_by_term=1

    34. LSUS Course Descriptions For Computer Science
    processor implementation techniques, pipelining, parallel processing, CSC 711 Introduction to computer science for Teachers 3 cr.
    http://www.lsus.edu/catalogs/catalog9798/catcsc.htm
    COMPUTER SCIENCE CSC 101: Indtroduction to the Internet 3 cr.
    Introduction to the fundamentals of the Internet as well as the fundamentals of data communications. Students will learn to use the Internet for research and communication, including publishing materials on the World Wide Web. Three hours of lecture. CSC 111: Introduction to Computing 3 cr.
    A survey of computing terminology and computing applications. Hands on activities using an integrated software package for word processing, spreadsheets and database management. Introduction to the Internet with applications. Three hours of lecture. CSC 112: Structured Programming 3 cr.
    Prerequisites: Credit for or registration in MATH 121 as well as computer literacy equivalent to CSC 111. Problem solving and algorithm development using a specific high-level computer programming language. The design, coding, debugging and documenting of programs using techniques of good programming style. Three hours of lecture. CSC 140: FORTRAN Programming 3 cr.
    Prerequisites: CSC 111 and MATH 121, or consent of the department. An introduction to problem solving and programming of scientific, statistical, and business problems using FORTRAN. Three hours of lecture.

    35. COMPUTER SCIENCE
    computer science CSC 101 Introduction to the Internet 3 cr. processorimplementation techniques, pipelining, parallel processing, distributed computing
    http://www.lsus.edu/catalogs/catalog9899/catcsc.htm
    COMPUTER SCIENCE
    CSC 101: Introduction to the Internet 3 cr.
    Introduction to the fundamentals of the Internet as well as the fundamentals of data communications. Students will learn to use the Internet for research and communication, including publishing materials on the World Wide Web. Three hours of lecture. CSC 105: Introduction to Computer-based Multimedia 3 cr.
    Introduction to the fundamentals of computer-based multimedia technologies and to the use of authoring applications and tools for creating and manipulating multimedia content. One application area covered will be the creation of internet Web pages. Three hours of lecture. CSC 111: Introduction to Computing 3 cr.
    A survey of computing terminology and computing applications. Hands on activities using an integrated software package for word processing, spreadsheets and database management. Introduction to the Internet with applications. Three hours of lecture. CSC 112: Structured Programming 3 cr.
    Prerequisites: Credit for or registration in MATH 121 as well as computer literacy equivalent to
    CSC 111. Problem solving and algorithm development using a specific high-level computer programming language. The design, coding, debugging and documenting of programs using techniques of good programming style. Three hours of lecture.

    36. MTU Department Of Computer Science
    Rong Ge Department of computer science Michigan Technological University However, software pipelining also brings a large register demand.
    http://cs.mtu.edu/html/abstracts/rong_ge_proposal.html
    Predicting the Effects of Scalar Replacement On Register Aloocation for Software Pipelined Loops
    Rong Ge
    Department of Computer Science
    Michigan Technological University
    Wednesday, March 13 at 4:00 PM in Fisher 126
    ABSTRACT
    Since the advent of ILP (Instruction-level Parallelism) processors, people have been trying to exploit the parallelism that exists at the operation level. Software pipelining is an excellent method for improving the parallelism in loops by overlapping operations from various loop iterations.
    However, software pipelining also brings a large register demand. Since the operations from different iterations are scheduled together, a value could need multiple copies to keep it live long enough to reach its last reference. In the case that the lifetime of a register is longer than the length of software pipelined loop body, multiple copies of this register are needed. The increase in register demand could be tremendous when a long schedule is wrapped and fitted into a small software pipelined body. If the register demand exceeds the number of registers available on the machine, some values have to be stored back to memory to make room for others. A better register pressure prediction scheme must be developed in order to take fully advantage of the benefit of software pipelining.
    Decreasing execution time is the goal of compiler optimization. To achieve this goal, memory operations are big concerns, especially in loops, because array operations appear in a loop very often. Failing to recognize memory reuse will cause a great number of memory accesses, thereby extending the loop's execution time. Scalar replacement, by replacing array variables with scalars, can effectively reduce the memory resource demand in innermost loop. However, for keeping the right semantics, an array variable could be replaced by more than one scalar variable. This can tremendously increase the register demand. So correctly estimating register pressure to avoid being over aggressive with scalar replacement becomes very important.

    37. MTU Department Of Computer Science
    Unfortunately, in a typical computer science curriculum, computing with Instruction scheduling in general, and software pipelining in particular face
    http://cs.mtu.edu/html/trs.html
    Technical Reports Stable Predicate Evaluation with Probabilistically Synchronized Clocks CS-TR-99-3 The evaluation of a global state in a distributed system is very difficult, since the individual processes that comprise the system share no common memory or time base, and can only communicate with each other via message passing. Although no common time base exists in these systems, the system clocks are often roughly synchronized within some known upper bound. In previous work, Mayo and Kearns developed a schema for evaluating a class of stable predicates on systems with a rough global time base. These global predicates are comprised of the conjunction of the local process states. The fact that the predicates are stable means that once they become true, they remain true forever. The ability to detect stable predicates in the system allows us to detect critical system states such as program termination and deadlock. We propose to develop a protocol based on Mayo and Kearns's schema, which will also handle systems where clocks are synchronized with a probabilistic clock synchronization protocol. Also, our protocol will allow processes to enter and leave the system, facilitating its use in dynamic systems. Finally, we plan to implement our protocol on an actual system in order to see how it performs in general use. Register Assignment for Software Pipelining with Partitioned Register Banks CS-TR 99-2 Trends in instruction-level parallelism (ILP) are putting increased demands on a machine's register resources. Computer architects are adding increased numbers of functional units to allow more instructions to be executed in parallel, thereby increasing the number of register ports needed. This increase in ports hampers access time. Additionally, aggressive scheduling techniques, such as software pipelining, are requiring more registers to attain high levels of ILP. These two factors make it difficult to maintain a single monolithic register bank.

    38. Computer Science, Rutgers University: [198:505 ] Advanced Computer Architecture
    Objectives Core material for computer science degree candidates. OutlineAdvanced computer arithmetic Performance pipelining Vector processing
    http://www.cs.rutgers.edu/cs/academics/graduate/courses/node11.html
    Search CS site
    Search WWW
    Maintained by web@cs.rutgers.edu
    [198:505 ] Advanced Computer Architecture
    Credits:
    Instructor:
    S. Levy, M. Murdocca, M. Paull, or staff
    Schedule: Fall and Spring semesters
    Objectives
    Core material for Computer Science degree candidates. The course is designed to provide a solid understanding of the architecture, organization, and design of digital systems. The emphasis is on theoretical issues rather than on the physical hardware. Advanced topics are covered such as pipelining, parallel architecture, and communication.
    Prerequisites
    Entrance requirements, and a course that covers fundamentals of computer architecture such as combinational and sequential logic design, data representation, memory management, assembly language, and microprogramming.
    Outline
    Advanced computer arithmetic
    Performance
    Pipelining
    Vector processing
    I/O and communication
    Parallel architecture
    Expected Work
    There will be regular homework problems, and two or three exams.
    References
    Computer Architecture: A Quantitative Approach , Morgan Kaufmann Publishers, 1990.

    39. Courses Offered By CSE Department, IIT Kanpur
    Advanced Concepts pipelining; Introduction to Advanced Processors. I II,computer science Press, 1988. Back to list of courses
    http://www.cse.iitk.ac.in/acad/courses1.html
    Course Descriptions
    ESc 101: Fundamentals of Computing
    This is a compulsory course for ALL undergraduate students. For course description, please see the undergraduate bulletin. Back to list of courses
    CS 100: Introduction to Profession
    Course Contents:
    Books and References:
    Back to list of courses
    CS 201: Discrete Mathematics
    Structure: 3-0-0-0 Academic Load=9 Weightage=3
    Course Contents:
    Notion of proof: proof by counter-example, the contrapositive, proof by contradiction, inductive proofs. Algebra: Motivation of algebraic structures; review of basic group theory with emphasis to finite groups: subgroups and group homomorphism, Lagrange's theorem. Commutative rings, ideals. Finite fields and their elementary properties. Some CS applications (e.g., RSA, error correcting codes). Combinatorics: Basic counting techniques, pigeon-hole principle, recurrence relations, generating functions, Polya's counting theorem. Basics of graph theory. Introduction to probabilistic method in combinatorics. Formal logic: Propositional logic: proof system, semantics, completeness, compactness. Length of proofs, polynomial size proofs, efficiency of proof systems. First order logic: models, proof system, compactness. Examples of formal proofs in, say, number theory or group theory. Some advanced topics. E.g., CS application of logic, introduction to modal and temporal logics, Or, formal number theory including incompleteness theorem, Or, elements of proof theory including cut elimination, Or zero-one law for first order logic.

    40. Pipelining With Futures
    pipelining with futures. Full text, pdf format Pdf (1.73 MB) Margaret ReidMiller,School of computer science, Carnegie Mellon University, Pittsburgh,
    http://portal.acm.org/citation.cfm?id=258517

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