Machines and languages theory. Lecture 1

Size: px
Start display at page:

Download "Machines and languages theory. Lecture 1"

Transcription

1 Machines and languages theory Lecture 1

2 Machines and languages theory Instructor: Fatemeh Daneshfar TA:? Text: An Introduction to Formal Languages and Automata, (5th ed.) - Linz (Jones & Bartlett) Webpage:

3 Machines and languages theory Requirements: 30% - Exam1 (the 21 th Aban) 30% - Exam2 (the 26 th Azar) 40% - Final Exam (two hours) cumulative. 5% - Presentation Students may not do extra credit work to make up for missing exams or poor exam grades.

4 Course overview The course discusses two very closely related concepts: models of computing and languages The computing models are simplified as much as possible, so as to boil them down to their most important elements. Some of the models will be more powerful than others. Languages are effectively sets of strings which are built by particular rules, called a grammar. The more complex the grammar, the more complicated the language can be. 4

5 Models of computing Finite state machines (automata) Pattern recognition Simple circuits (e.g. elevators, sliding doors) Automata with stack memory (pushdown automata.) Parsing computer languages Automata with limited tape memory Automata with infinite tape memory called `Turing machines Most powerful model possible Capable of solving anything that is solvable 5

6 Chomsky hierarchy of grammars Regular grammars Context free grammars Context sensitive grammars Unrestricted grammars We ll define what these mean later, but the important point is that the grammars become more complex as we go down the list, and contain those above it. 6

7 Computers recognise languages! Computers can be made to recognize, or accept, the strings of a language. There is a correspondence between the power of the computing model and the complexity of languages that it can recognize! Finite automata only accept regular grammars. Push down automata can also accept context free grammars. Turing machines can accept all grammars. This is why we study both in this course! 7

8 Week Section Syllabus Topic Mathematical Preliminaries Basic Concepts 2.1 Deterministic Finite Automata (dfa) Nondeterministic Finite Automata (ndfa) 2.3 Equivalence of dfa's and ndfa's

9 Week Section Syllabus Topic Regular Expressions (re) Connection between re's and Regular Languages 3.3 Regular Grammars Closure Properties of Regular Languages 4.2 Elementary Questions about Regular Languages Identifying Nonregular Languages

10 Week Section Syllabus Topic Context-free Grammars (cfg) 5.2 Parsing and Ambiguity Chomsky and Greibach Normal Forms for cfg's 7.1 Nondeterministic Pushdown Automata (pda) 7.2 Pda's and Context-free Grammars Pumping Lemma for Context-free Languages 8.2 Closure Properties of Context-free Languages

11 Week Section Syllabus Topic Turing Machines 9.2 More on Turing Machines Turing's Thesis 11.1 Recursive and Recursively Enumerable Languages The Chomsky Hierarchy 12.1 Unsolvable Problems Undecidable Problems for Rec. Enum. Languages 15 Final Exam

12 Chapter 1 Introduction to the Theory of Computing

13 Introduction to the Theory of Computing Mathematical Preliminaries and Notation Sets Functions and Relations Graphs and Trees Proof Techniques

14 Mathematical Preliminaries and Notation Sets notation {1, 2, 3, 4, 5}, {1, 2,..., 5}, {x 1 x 5} membership 3 S 7 S an apple S

15 Mathematical Preliminaries and Notation Sets union and intersection know what U (union) and (intersection) mean universal set understand that the universal set is merely ALL the things that are under discussion. implicit vs. explicit

16 Mathematical Preliminaries and Sets complement Notation The complement of S, written as S', (S with a bar over it in the book) is all the elements of the universe not in S difference The difference between S and T = S T = S T'

17 Mathematical Preliminaries and Notation empty (null) set The empty set ϕ is the set containing no elements

18 Mathematical Preliminaries and Notation demorgan's Laws (S' T')' = S U T (S' U T')' = S T

19 Mathematical Preliminaries and subset Notation S T iff every element in S is also in T S T (S is a proper subset of T) if S T and there is something in T that is not in S disjoint Two sets are disjoint if their intersection is empty; they have no elements in common

20 Mathematical Preliminaries and infinite vs. finite sets Notation A set is infinite if it is not possible to list all of the elements. There are two classes of infinity: numerable, not enumerable This will become very important in this class

21 Mathematical Preliminaries and powerset Notation The powerset of a set S (written as 2 S ) is the set of all the subsets of the set S There's a reason for the notation

22 Mathematical Preliminaries and Cartesian product Notation The Cartesian product of two sets S and T, written as S T, is the set of all the ordered pairs created by choosing one element of S and one element of T.

23 Mathematical Preliminaries and Functions Notation A function f : S T is the mapping of elements of S to unique elements of T domain, range

24 Mathematical Preliminaries and Relations Notation A relation between S and T is a set of ordered pairs (s, t) taken from these sets. A relation is a subset of Cartesian product of S and T. A function is a special kind of relation reflexive, symmetric, transitive A relation that is reflexive, symmetric and transitive is called an equivalence relation and partitions the underlying set.

25 Mathematical Preliminaries and Notation Graphs and Trees Read the section and learn the notation

26 Mathematical Preliminaries and Notation Proof Techniques proof by contradiction proofs Mathematical induction

27 Mathematical Preliminaries and Notation Mathematical induction Prove that the sum of all integers between 1 and n = n(n + 1) / 2.

28 Mathematical Preliminaries and Notation Prove that the sum of all integers between 1 and n = n(n + 1) / 2 for all n. Basis: Consider n = 1. The sum of all integers from 1 to 1 is 1. But (1)(2)/2 = 1 also. Proven for this case Hypothesis: Assume that the sum of all integers from 1 to n is n(n + 1) / 2

29 Mathematical Preliminaries and Notation Prove that the sum of all integers between 1 and n = n(n + 1) / 2 for all n. Induction: We will show that it is true for n + 1, where n is the number from the hypothesis. The sum of the integers from 1 to n + 1 is the same as the sum of the integers from 1 to n, plus n + 1. From the hypothesis, this is n(n+1)/2 + n + 1. A little algebra show us that this is (n + 1)(n + 2)/2. Done!

30 Introduction to the Theory of Three Basic Concepts Languages: Computing An alphabet is a finite set of symbols. = {a, b} A string or word is any series of symbols from the alphabet. w = abaaa : empty string *: the set of all strings on ( + = * { }) A language is any set of words (a subset L of *). Sentence: a string in L

31 Languages A language is a set of strings. If is an alphabet, then a language over is a collection of strings whose components come from. So * isthebiggest possible language over, and every other language over is a subset of *. 31

32 Examples of languages Four simple examples of languages over an alphabet are the sets,{ },, and *. For example, if ={a} then these four simple languages over are, { }, {a}, and {, a, aa, aaa, }. Recall { } is the empty string while is the empty set. * is an infinite set. 32

33 Example: English The alphabet is A = {a,b,c,d,e x,y,z} The English language is made of strings formed from A: e.g. fun, excitement. We could define the English Language as the set of strings over A which appear in the Oxford English dictionary (but it is clearly not a unique definition). 33

34 Other Examples = {a, b} * = {, a, b, aa, ab, ba, aaa,...} L 1 = {a, aa, aab} (finite language) L 2 = {a n b n n 0} = {, ab, aabb,...} 34

35 Concatenation The natural operation of concatenation of strings places two strings in juxtaposition. For example, if then the concatenation of the two strings aab and ba is the string aabba. Use the name "cat " to denote this operation. cat(aab, ba) = aabba. 35

36 Combining Languages Also we can combine two languages L and M by forming the set of all concatenations of strings in L with strings in M. 36

37 Products of languages This new language is called the product of L and M and is denoted by L M. A formal definition can be given as follows: L M = {cat(s, t) s L and t M}. L1L2 = {xy x L1, y L2} For example, if L = {ab, ac} and M = {a, bc, abc}, then the product L M is the language L M = {aba, abbc, ababc, aca, acbc, acabc}. 37

38 Properties of products The following simple properties hold for any language L: L { } = { } L = L. L =.L =. The product is not commutative. In other words, we can find two languages L and M such that L M M L. The product is associative. In other words, if L, M, and N are languages, then L (M N) = (L M) N 38

39 Powers of languages If L is a language, then the product L L is denoted by L 2. The language product L n for every n {0, 1, 2, } is as follows: L 0 = { } L n = L L n-1 if n > 0 39

40 Example For example, if L = { a, bb} then the first few powers of L are L 0 = { } L 1 = L = {a, bb} L 2 = L L = {aa, abb, bba, bbbb} L 3 = L L 2 = {aaa, aabb, abba, abbbb, bbaa, bbabb, bbbba, bbbbbb} 40

41 Languages Example 2: L = {a n b n n 0} 41

42 Languages Example 2: L = {a n b n n 0} L 2 = {a n b n a m b m n 0, m 0} 42

43 Closure of a language If L is a language over (i.e. L *) then the closure of L is the language denoted by L* and is defined as follows: L* = L 0 L 1 L 2. The positive closure of L is the language denoted by L + and defined as follows: L + = L 1 L 2 L 3. 43

44 L* vs. L + It follows that L* =L + { }. But it s not necessarily true that L + = L* - { }. For example, if we let our alphabet be ={a} and our language be L ={, a}, then L + = L*. 44

45 Properties of Closure Let L and M be languages over the alphabet. Then: a) { }* = * = { } b) L* = L* L* = (L*)* c) L if and only if L + = L* d) (L* M*)* = (L* M*)* = (L M)* e) L (M L)* = (L M)* L 45

46 Grammars A grammar for a natural language tells us whether a particular sentence is well-formed or not. <sentence> <noun-phrase><predicate> <noun-phrase> <article><noun> <predicate> <verb> <article> a the <noun> boy dog <verb> runs walks 46

47 Three Basic Concepts Grammars A grammar is a finite set of rules (called productions) over an alphabet and a set of variables (non-terminals) to define the structure of the strings in a language. rule: where and are any string containing symbols from the alphabet and variables from the set of variables Start Symbol. One variable is set special. It's called the start symbol

48 Grammars Formal grammar: G = (V, T, S, P) V: finite set of variables T: finite set of terminal symbols S V: start variable P: finite set of productions 48

49 Productions A grammar rule is often called a production, and it can be read in any of severalwaysasfollows: "replace by ", produces," " rewrites to, " reduces to." 49

50 Grammars Productions: x y x (V T) + y (V T) * w = uxv derives z = uyv w z w 1 * w n (w 1 w 2... w n w 1 = w n ) w 1 + w n 50

51 Other shorthand: The following three symbols with their associated meanings are used quite often in discussing derivations: derives in one step, + derives in one or more steps, * derives in zero or more steps. 51

52 Where to begin Every grammar has a special grammar symbol called a start symbol, and there must be at least one production with left side consisting of only the start symbol. For example, if S is the start symbol for a grammar, then there must be at least one production of the form S. 52

53 Grammars Generated language: Derivation: G = (V, T, S, P) L(G) = {w T * S * w} S w 1 w 2... w n w L(G) Sentential forms: S, w 1,w 2,..., w n (containing variables) 53

54 Grammars Example 3: G = ({S}, {a, b}, S, P) P: S asb S S asb aasbb aabb aabb: sentence aasbb: sentential form 54

55 Grammars Example 3: G = ({S}, {a, b}, S, P) P: S asb S 55

56 Grammars Example 3: G = ({S}, {a, b}, S, P) P: S asb S L(G) = {a n b n n 0} L(G) = {a n b n+1 n 0}? 56

57 Grammars Example 4: 57

58 Grammars Example 5: G 2 = ({S}, {a, b}, S, P 2 ) P 2 : S SS S S asb S bsa 58

59 Grammars Example 5: G 2 = ({S}, {a, b}, S, P 2 ) P 2 : S SS S S asb S bsa L(G 2 ) = {w n a (w) = n b (w)} 59

60 Example Let A = {a, b, c}. Then a grammar for the language A* can be described by the following four productions: S S as S bs S cs. Or in shorthand: S as bs cs, "S can be replaced by either, or as, or bs, or cs." 60

61 Sample derivation. S as bs cs, S as S as aas. S as aas aacs aacbs.. S as aas aacs aacbs aacb = aacb A short hand way of showing a derivation exists: S * aacb derives in zero or more steps 61

62 A more complex grammar S AB A aa B bb. We can deduce that the grammar non-terminal symbols are S, A, and B, the start symbol is S, and the language alphabet includes, a, and b. 62

63 Another derivation Let's consider the string aab. The statement S + aab means that there exists a derivation of aab that takes one or more steps. For example, we have S AB aab aaab aab aabb aab. 63

64 Introduction to the Theory of Computing

65 Introduction to the Theory of Computing

66 Finite languages If the language is finite, then a grammar can consist of all productions of the form S w for each string w in the language. For example, the language {a, ba} can be described by the grammar S a ab. 66

67 Infinite languages If the language is infinite, then some production or sequence of productions must be used repeatedly to construct the derivations. Notice that there is no bound on the length of strings in an infinite language. Therefore there is no bound on the number of derivation steps used to derive the strings. If the grammar has n productions, then any derivation consisting of n + 1 steps must use some production twice 67

68 For example, the infinite language {a n b n 0}canbe described by the grammar, S b as. To derive the string a n b, use the production S as repeatedly --n times to be exact-- and then stop the derivation by using the production S b. The production S as allows us to say If S derives w, then it also derives aw," 68

69 Some simple grammars Language Grammar {a, ab, abb, abbb} S a ab abb abbb {, a, aa, aaa, } S as {b, bbb, bbbbb, b 2n+1 } S bbs b {b, abc, aabcc,, a n bc n } S asc b {ac, abc, abbc,, ab n c} S abc B bb 69

70 Automata An abstract model of digital computer: Input file Control unit Storage Output 70

71 Automata Input file: is divided into squares. Input is a string over a given alphabet. Each input square holds a symbol. The symbols are read from left to right, one at a time. The end of the input string can be detected. 71

72 Automata Storage: consists of an unlimited number of cells. Each cell can hold a symbol from an alphabet (which can be different from the input alphabet). The contents of the storage cells can be read and changed. 72

73 Automata Control unit: has a finite number of internal states. Can be in any one of the internal states. Can change state in some defined manner. 73

74 Automata Transition function: current state input symbol storage info next state Output may be produced Info in the storage may be changed Configuration: current state input symbol storage info Move: current configuration next configuration 74

75 Automata General types of automata: Accepter: yes/no output Transducer: string of symbols as output Deterministic: single move Non-deterministic: multiple moves 75

76 Homework Exercises: 4, 5, 6, 8, 9, 12, 15, 17 of Section Linz s book. Reading: Section Linz s book. 76

Language properties and Grammar of Parallel and Series Parallel Languages

Language properties and Grammar of Parallel and Series Parallel Languages arxiv:1711.01799v1 [cs.fl] 6 Nov 2017 Language properties and Grammar of Parallel and Series Parallel Languages Mohana.N 1, Kalyani Desikan 2 and V.Rajkumar Dare 3 1 Division of Mathematics, School of

More information

Informatics 2A: Language Complexity and the. Inf2A: Chomsky Hierarchy

Informatics 2A: Language Complexity and the. Inf2A: Chomsky Hierarchy Informatics 2A: Language Complexity and the Chomsky Hierarchy September 28, 2010 Starter 1 Is there a finite state machine that recognises all those strings s from the alphabet {a, b} where the difference

More information

A General Class of Noncontext Free Grammars Generating Context Free Languages

A General Class of Noncontext Free Grammars Generating Context Free Languages INFORMATION AND CONTROL 43, 187-194 (1979) A General Class of Noncontext Free Grammars Generating Context Free Languages SARWAN K. AGGARWAL Boeing Wichita Company, Wichita, Kansas 67210 AND JAMES A. HEINEN

More information

COMPUTATIONAL COMPLEXITY OF LEFT-ASSOCIATIVE GRAMMAR

COMPUTATIONAL COMPLEXITY OF LEFT-ASSOCIATIVE GRAMMAR COMPUTATIONAL COMPLEXITY OF LEFT-ASSOCIATIVE GRAMMAR ROLAND HAUSSER Institut für Deutsche Philologie Ludwig-Maximilians Universität München München, West Germany 1. CHOICE OF A PRIMITIVE OPERATION The

More information

A R "! I,,, !~ii ii! A ow ' r.-ii ' i ' JA' V5, 9. MiN, ;

A R ! I,,, !~ii ii! A ow ' r.-ii ' i ' JA' V5, 9. MiN, ; A R "! I,,, r.-ii ' i '!~ii ii! A ow ' I % i o,... V. 4..... JA' i,.. Al V5, 9 MiN, ; Logic and Language Models for Computer Science Logic and Language Models for Computer Science HENRY HAMBURGER George

More information

A Version Space Approach to Learning Context-free Grammars

A Version Space Approach to Learning Context-free Grammars Machine Learning 2: 39~74, 1987 1987 Kluwer Academic Publishers, Boston - Manufactured in The Netherlands A Version Space Approach to Learning Context-free Grammars KURT VANLEHN (VANLEHN@A.PSY.CMU.EDU)

More information

Proof Theory for Syntacticians

Proof Theory for Syntacticians Department of Linguistics Ohio State University Syntax 2 (Linguistics 602.02) January 5, 2012 Logics for Linguistics Many different kinds of logic are directly applicable to formalizing theories in syntax

More information

Syntax Parsing 1. Grammars and parsing 2. Top-down and bottom-up parsing 3. Chart parsers 4. Bottom-up chart parsing 5. The Earley Algorithm

Syntax Parsing 1. Grammars and parsing 2. Top-down and bottom-up parsing 3. Chart parsers 4. Bottom-up chart parsing 5. The Earley Algorithm Syntax Parsing 1. Grammars and parsing 2. Top-down and bottom-up parsing 3. Chart parsers 4. Bottom-up chart parsing 5. The Earley Algorithm syntax: from the Greek syntaxis, meaning setting out together

More information

Probability and Game Theory Course Syllabus

Probability and Game Theory Course Syllabus Probability and Game Theory Course Syllabus DATE ACTIVITY CONCEPT Sunday Learn names; introduction to course, introduce the Battle of the Bismarck Sea as a 2-person zero-sum game. Monday Day 1 Pre-test

More information

RANKING AND UNRANKING LEFT SZILARD LANGUAGES. Erkki Mäkinen DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF TAMPERE REPORT A ER E P S I M S

RANKING AND UNRANKING LEFT SZILARD LANGUAGES. Erkki Mäkinen DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF TAMPERE REPORT A ER E P S I M S N S ER E P S I M TA S UN A I S I T VER RANKING AND UNRANKING LEFT SZILARD LANGUAGES Erkki Mäkinen DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF TAMPERE REPORT A-1997-2 UNIVERSITY OF TAMPERE DEPARTMENT OF

More information

Grammars & Parsing, Part 1:

Grammars & Parsing, Part 1: Grammars & Parsing, Part 1: Rules, representations, and transformations- oh my! Sentence VP The teacher Verb gave the lecture 2015-02-12 CS 562/662: Natural Language Processing Game plan for today: Review

More information

Natural Language Processing. George Konidaris

Natural Language Processing. George Konidaris Natural Language Processing George Konidaris gdk@cs.brown.edu Fall 2017 Natural Language Processing Understanding spoken/written sentences in a natural language. Major area of research in AI. Why? Humans

More information

Spring 2016 Stony Brook University Instructor: Dr. Paul Fodor

Spring 2016 Stony Brook University Instructor: Dr. Paul Fodor CSE215, Foundations of Computer Science Course Information Spring 2016 Stony Brook University Instructor: Dr. Paul Fodor http://www.cs.stonybrook.edu/~cse215 Course Description Introduction to the logical

More information

Erkki Mäkinen State change languages as homomorphic images of Szilard languages

Erkki Mäkinen State change languages as homomorphic images of Szilard languages Erkki Mäkinen State change languages as homomorphic images of Szilard languages UNIVERSITY OF TAMPERE SCHOOL OF INFORMATION SCIENCES REPORTS IN INFORMATION SCIENCES 48 TAMPERE 2016 UNIVERSITY OF TAMPERE

More information

Context Free Grammars. Many slides from Michael Collins

Context Free Grammars. Many slides from Michael Collins Context Free Grammars Many slides from Michael Collins Overview I An introduction to the parsing problem I Context free grammars I A brief(!) sketch of the syntax of English I Examples of ambiguous structures

More information

Enumeration of Context-Free Languages and Related Structures

Enumeration of Context-Free Languages and Related Structures Enumeration of Context-Free Languages and Related Structures Michael Domaratzki Jodrey School of Computer Science, Acadia University Wolfville, NS B4P 2R6 Canada Alexander Okhotin Department of Mathematics,

More information

CS 598 Natural Language Processing

CS 598 Natural Language Processing CS 598 Natural Language Processing Natural language is everywhere Natural language is everywhere Natural language is everywhere Natural language is everywhere!"#$%&'&()*+,-./012 34*5665756638/9:;< =>?@ABCDEFGHIJ5KL@

More information

Lecture 10: Reinforcement Learning

Lecture 10: Reinforcement Learning Lecture 1: Reinforcement Learning Cognitive Systems II - Machine Learning SS 25 Part III: Learning Programs and Strategies Q Learning, Dynamic Programming Lecture 1: Reinforcement Learning p. Motivation

More information

On the Polynomial Degree of Minterm-Cyclic Functions

On the Polynomial Degree of Minterm-Cyclic Functions On the Polynomial Degree of Minterm-Cyclic Functions Edward L. Talmage Advisor: Amit Chakrabarti May 31, 2012 ABSTRACT When evaluating Boolean functions, each bit of input that must be checked is costly,

More information

Self Study Report Computer Science

Self Study Report Computer Science Computer Science undergraduate students have access to undergraduate teaching, and general computing facilities in three buildings. Two large classrooms are housed in the Davis Centre, which hold about

More information

11/29/2010. Statistical Parsing. Statistical Parsing. Simple PCFG for ATIS English. Syntactic Disambiguation

11/29/2010. Statistical Parsing. Statistical Parsing. Simple PCFG for ATIS English. Syntactic Disambiguation tatistical Parsing (Following slides are modified from Prof. Raymond Mooney s slides.) tatistical Parsing tatistical parsing uses a probabilistic model of syntax in order to assign probabilities to each

More information

The Strong Minimalist Thesis and Bounded Optimality

The Strong Minimalist Thesis and Bounded Optimality The Strong Minimalist Thesis and Bounded Optimality DRAFT-IN-PROGRESS; SEND COMMENTS TO RICKL@UMICH.EDU Richard L. Lewis Department of Psychology University of Michigan 27 March 2010 1 Purpose of this

More information

Objectives. Chapter 2: The Representation of Knowledge. Expert Systems: Principles and Programming, Fourth Edition

Objectives. Chapter 2: The Representation of Knowledge. Expert Systems: Principles and Programming, Fourth Edition Chapter 2: The Representation of Knowledge Expert Systems: Principles and Programming, Fourth Edition Objectives Introduce the study of logic Learn the difference between formal logic and informal logic

More information

Standard 1: Number and Computation

Standard 1: Number and Computation Standard 1: Number and Computation Standard 1: Number and Computation The student uses numerical and computational concepts and procedures in a variety of situations. Benchmark 1: Number Sense The student

More information

Genevieve L. Hartman, Ph.D.

Genevieve L. Hartman, Ph.D. Curriculum Development and the Teaching-Learning Process: The Development of Mathematical Thinking for all children Genevieve L. Hartman, Ph.D. Topics for today Part 1: Background and rationale Current

More information

Basic Parsing with Context-Free Grammars. Some slides adapted from Julia Hirschberg and Dan Jurafsky 1

Basic Parsing with Context-Free Grammars. Some slides adapted from Julia Hirschberg and Dan Jurafsky 1 Basic Parsing with Context-Free Grammars Some slides adapted from Julia Hirschberg and Dan Jurafsky 1 Announcements HW 2 to go out today. Next Tuesday most important for background to assignment Sign up

More information

TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system

TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system Curriculum Overview Mathematics 1 st term 5º grade - 2010 TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system Multiplies and divides decimals by 10 or 100. Multiplies and divide

More information

"f TOPIC =T COMP COMP... OBJ

f TOPIC =T COMP COMP... OBJ TREATMENT OF LONG DISTANCE DEPENDENCIES IN LFG AND TAG: FUNCTIONAL UNCERTAINTY IN LFG IS A COROLLARY IN TAG" Aravind K. Joshi Dept. of Computer & Information Science University of Pennsylvania Philadelphia,

More information

WSU Five-Year Program Review Self-Study Cover Page

WSU Five-Year Program Review Self-Study Cover Page WSU Five-Year Program Review Self-Study Cover Page Department: Program: Computer Science Computer Science AS/BS Semester Submitted: Spring 2012 Self-Study Team Chair: External to the University but within

More information

Statewide Framework Document for:

Statewide Framework Document for: Statewide Framework Document for: 270301 Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance

More information

A Minimalist Approach to Code-Switching. In the field of linguistics, the topic of bilingualism is a broad one. There are many

A Minimalist Approach to Code-Switching. In the field of linguistics, the topic of bilingualism is a broad one. There are many Schmidt 1 Eric Schmidt Prof. Suzanne Flynn Linguistic Study of Bilingualism December 13, 2013 A Minimalist Approach to Code-Switching In the field of linguistics, the topic of bilingualism is a broad one.

More information

What the National Curriculum requires in reading at Y5 and Y6

What the National Curriculum requires in reading at Y5 and Y6 What the National Curriculum requires in reading at Y5 and Y6 Word reading apply their growing knowledge of root words, prefixes and suffixes (morphology and etymology), as listed in Appendix 1 of the

More information

CS 101 Computer Science I Fall Instructor Muller. Syllabus

CS 101 Computer Science I Fall Instructor Muller. Syllabus CS 101 Computer Science I Fall 2013 Instructor Muller Syllabus Welcome to CS101. This course is an introduction to the art and science of computer programming and to some of the fundamental concepts of

More information

Lecture 1: Machine Learning Basics

Lecture 1: Machine Learning Basics 1/69 Lecture 1: Machine Learning Basics Ali Harakeh University of Waterloo WAVE Lab ali.harakeh@uwaterloo.ca May 1, 2017 2/69 Overview 1 Learning Algorithms 2 Capacity, Overfitting, and Underfitting 3

More information

ENGBG1 ENGBL1 Campus Linguistics. Meeting 2. Chapter 7 (Morphology) and chapter 9 (Syntax) Pia Sundqvist

ENGBG1 ENGBL1 Campus Linguistics. Meeting 2. Chapter 7 (Morphology) and chapter 9 (Syntax) Pia Sundqvist Meeting 2 Chapter 7 (Morphology) and chapter 9 (Syntax) Today s agenda Repetition of meeting 1 Mini-lecture on morphology Seminar on chapter 7, worksheet Mini-lecture on syntax Seminar on chapter 9, worksheet

More information

Developing a concrete-pictorial-abstract model for negative number arithmetic

Developing a concrete-pictorial-abstract model for negative number arithmetic Developing a concrete-pictorial-abstract model for negative number arithmetic Jai Sharma and Doreen Connor Nottingham Trent University Research findings and assessment results persistently identify negative

More information

Grade 6: Correlated to AGS Basic Math Skills

Grade 6: Correlated to AGS Basic Math Skills Grade 6: Correlated to AGS Basic Math Skills Grade 6: Standard 1 Number Sense Students compare and order positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and

More information

Morphotactics as Tier-Based Strictly Local Dependencies

Morphotactics as Tier-Based Strictly Local Dependencies Morphotactics as Tier-Based Strictly Local Dependencies Alëna Aksënova, Thomas Graf, and Sedigheh Moradi Stony Brook University SIGMORPHON 14 Berlin, Germany 11. August 2016 Our goal Received view Recent

More information

South Carolina English Language Arts

South Carolina English Language Arts South Carolina English Language Arts A S O F J U N E 2 0, 2 0 1 0, T H I S S TAT E H A D A D O P T E D T H E CO M M O N CO R E S TAT E S TA N DA R D S. DOCUMENTS REVIEWED South Carolina Academic Content

More information

Grade 5 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print

Grade 5 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 5 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology

More information

PRODUCT PLATFORM DESIGN: A GRAPH GRAMMAR APPROACH

PRODUCT PLATFORM DESIGN: A GRAPH GRAMMAR APPROACH Proceedings of DETC 99: 1999 ASME Design Engineering Technical Conferences September 12-16, 1999, Las Vegas, Nevada DETC99/DTM-8762 PRODUCT PLATFORM DESIGN: A GRAPH GRAMMAR APPROACH Zahed Siddique Graduate

More information

CS 1103 Computer Science I Honors. Fall Instructor Muller. Syllabus

CS 1103 Computer Science I Honors. Fall Instructor Muller. Syllabus CS 1103 Computer Science I Honors Fall 2016 Instructor Muller Syllabus Welcome to CS1103. This course is an introduction to the art and science of computer programming and to some of the fundamental concepts

More information

Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice

Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice Title: Considering Coordinate Geometry Common Core State Standards

More information

TabletClass Math Geometry Course Guidebook

TabletClass Math Geometry Course Guidebook TabletClass Math Geometry Course Guidebook Includes Final Exam/Key, Course Grade Calculation Worksheet and Course Certificate Student Name Parent Name School Name Date Started Course Date Completed Course

More information

Constraining X-Bar: Theta Theory

Constraining X-Bar: Theta Theory Constraining X-Bar: Theta Theory Carnie, 2013, chapter 8 Kofi K. Saah 1 Learning objectives Distinguish between thematic relation and theta role. Identify the thematic relations agent, theme, goal, source,

More information

Numeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C

Numeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C Numeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C Using and applying mathematics objectives (Problem solving, Communicating and Reasoning) Select the maths to use in some classroom

More information

Introduction to HPSG. Introduction. Historical Overview. The HPSG architecture. Signature. Linguistic Objects. Descriptions.

Introduction to HPSG. Introduction. Historical Overview. The HPSG architecture. Signature. Linguistic Objects. Descriptions. to as a linguistic theory to to a member of the family of linguistic frameworks that are called generative grammars a grammar which is formalized to a high degree and thus makes exact predictions about

More information

Lecture 1: Basic Concepts of Machine Learning

Lecture 1: Basic Concepts of Machine Learning Lecture 1: Basic Concepts of Machine Learning Cognitive Systems - Machine Learning Ute Schmid (lecture) Johannes Rabold (practice) Based on slides prepared March 2005 by Maximilian Röglinger, updated 2010

More information

Algebra 2- Semester 2 Review

Algebra 2- Semester 2 Review Name Block Date Algebra 2- Semester 2 Review Non-Calculator 5.4 1. Consider the function f x 1 x 2. a) Describe the transformation of the graph of y 1 x. b) Identify the asymptotes. c) What is the domain

More information

1/20 idea. We ll spend an extra hour on 1/21. based on assigned readings. so you ll be ready to discuss them in class

1/20 idea. We ll spend an extra hour on 1/21. based on assigned readings. so you ll be ready to discuss them in class If we cancel class 1/20 idea We ll spend an extra hour on 1/21 I ll give you a brief writing problem for 1/21 based on assigned readings Jot down your thoughts based on your reading so you ll be ready

More information

University of Groningen. Systemen, planning, netwerken Bosman, Aart

University of Groningen. Systemen, planning, netwerken Bosman, Aart University of Groningen Systemen, planning, netwerken Bosman, Aart IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document

More information

AQUA: An Ontology-Driven Question Answering System

AQUA: An Ontology-Driven Question Answering System AQUA: An Ontology-Driven Question Answering System Maria Vargas-Vera, Enrico Motta and John Domingue Knowledge Media Institute (KMI) The Open University, Walton Hall, Milton Keynes, MK7 6AA, United Kingdom.

More information

1 st Quarter (September, October, November) August/September Strand Topic Standard Notes Reading for Literature

1 st Quarter (September, October, November) August/September Strand Topic Standard Notes Reading for Literature 1 st Grade Curriculum Map Common Core Standards Language Arts 2013 2014 1 st Quarter (September, October, November) August/September Strand Topic Standard Notes Reading for Literature Key Ideas and Details

More information

DMA CLUSTER CALCULATIONS POLICY

DMA CLUSTER CALCULATIONS POLICY DMA CLUSTER CALCULATIONS POLICY Watlington C P School Shouldham Windows User HEWLETT-PACKARD [Company address] Riverside Federation CONTENTS Titles Page Schools involved 2 Rationale 3 Aims and principles

More information

Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology. Michael L. Connell University of Houston - Downtown

Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology. Michael L. Connell University of Houston - Downtown Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology Michael L. Connell University of Houston - Downtown Sergei Abramovich State University of New York at Potsdam Introduction

More information

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic

More information

Evolution of Collective Commitment during Teamwork

Evolution of Collective Commitment during Teamwork Fundamenta Informaticae 56 (2003) 329 371 329 IOS Press Evolution of Collective Commitment during Teamwork Barbara Dunin-Kȩplicz Institute of Informatics, Warsaw University Banacha 2, 02-097 Warsaw, Poland

More information

GUIDE TO THE CUNY ASSESSMENT TESTS

GUIDE TO THE CUNY ASSESSMENT TESTS GUIDE TO THE CUNY ASSESSMENT TESTS IN MATHEMATICS Rev. 117.016110 Contents Welcome... 1 Contact Information...1 Programs Administered by the Office of Testing and Evaluation... 1 CUNY Skills Assessment:...1

More information

Office Hours: Mon & Fri 10:00-12:00. Course Description

Office Hours: Mon & Fri 10:00-12:00. Course Description 1 State University of New York at Buffalo INTRODUCTION TO STATISTICS PSC 408 4 credits (3 credits lecture, 1 credit lab) Fall 2016 M/W/F 1:00-1:50 O Brian 112 Lecture Dr. Michelle Benson mbenson2@buffalo.edu

More information

IT Students Workshop within Strategic Partnership of Leibniz University and Peter the Great St. Petersburg Polytechnic University

IT Students Workshop within Strategic Partnership of Leibniz University and Peter the Great St. Petersburg Polytechnic University IT Students Workshop within Strategic Partnership of Leibniz University and Peter the Great St. Petersburg Polytechnic University 06.11.16 13.11.16 Hannover Our group from Peter the Great St. Petersburg

More information

Physics Experimental Physics II: Electricity and Magnetism Prof. Eno Spring 2017

Physics Experimental Physics II: Electricity and Magnetism Prof. Eno Spring 2017 Physics 276 - Experimental Physics II: Electricity and Magnetism Prof. Eno Spring 2017 Course information: Experimental methods and tools related to circuits. Topics include inductance, capacitance, AC

More information

OCR for Arabic using SIFT Descriptors With Online Failure Prediction

OCR for Arabic using SIFT Descriptors With Online Failure Prediction OCR for Arabic using SIFT Descriptors With Online Failure Prediction Andrey Stolyarenko, Nachum Dershowitz The Blavatnik School of Computer Science Tel Aviv University Tel Aviv, Israel Email: stloyare@tau.ac.il,

More information

Diagnostic Test. Middle School Mathematics

Diagnostic Test. Middle School Mathematics Diagnostic Test Middle School Mathematics Copyright 2010 XAMonline, Inc. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by

More information

16 WEEKS STUDY PLAN FOR BS(IT)2 nd Semester

16 WEEKS STUDY PLAN FOR BS(IT)2 nd Semester 16 WEEKS STUDY PLAN FOR BS(IT)2 nd Semester COURSE: OBJECT ORIENTED PROGRAMMING Week Ch# Chapter Names 1 1 The Big Picture 2 2 C++ Programming Basics 3 3 Loops and Decisions 4 4 Structures 5 4 Structures

More information

Chunk Parsing for Base Noun Phrases using Regular Expressions. Let s first let the variable s0 be the sentence tree of the first sentence.

Chunk Parsing for Base Noun Phrases using Regular Expressions. Let s first let the variable s0 be the sentence tree of the first sentence. NLP Lab Session Week 8 October 15, 2014 Noun Phrase Chunking and WordNet in NLTK Getting Started In this lab session, we will work together through a series of small examples using the IDLE window and

More information

Pre-Algebra A. Syllabus. Course Overview. Course Goals. General Skills. Credit Value

Pre-Algebra A. Syllabus. Course Overview. Course Goals. General Skills. Credit Value Syllabus Pre-Algebra A Course Overview Pre-Algebra is a course designed to prepare you for future work in algebra. In Pre-Algebra, you will strengthen your knowledge of numbers as you look to transition

More information

Are You Ready? Simplify Fractions

Are You Ready? Simplify Fractions SKILL 10 Simplify Fractions Teaching Skill 10 Objective Write a fraction in simplest form. Review the definition of simplest form with students. Ask: Is 3 written in simplest form? Why 7 or why not? (Yes,

More information

Compositional Semantics

Compositional Semantics Compositional Semantics CMSC 723 / LING 723 / INST 725 MARINE CARPUAT marine@cs.umd.edu Words, bag of words Sequences Trees Meaning Representing Meaning An important goal of NLP/AI: convert natural language

More information

Lecture 2: Quantifiers and Approximation

Lecture 2: Quantifiers and Approximation Lecture 2: Quantifiers and Approximation Case study: Most vs More than half Jakub Szymanik Outline Number Sense Approximate Number Sense Approximating most Superlative Meaning of most What About Counting?

More information

State University of New York at Buffalo INTRODUCTION TO STATISTICS PSC 408 Fall 2015 M,W,F 1-1:50 NSC 210

State University of New York at Buffalo INTRODUCTION TO STATISTICS PSC 408 Fall 2015 M,W,F 1-1:50 NSC 210 1 State University of New York at Buffalo INTRODUCTION TO STATISTICS PSC 408 Fall 2015 M,W,F 1-1:50 NSC 210 Dr. Michelle Benson mbenson2@buffalo.edu Office: 513 Park Hall Office Hours: Mon & Fri 10:30-12:30

More information

(Sub)Gradient Descent

(Sub)Gradient Descent (Sub)Gradient Descent CMSC 422 MARINE CARPUAT marine@cs.umd.edu Figures credit: Piyush Rai Logistics Midterm is on Thursday 3/24 during class time closed book/internet/etc, one page of notes. will include

More information

Parallel Evaluation in Stratal OT * Adam Baker University of Arizona

Parallel Evaluation in Stratal OT * Adam Baker University of Arizona Parallel Evaluation in Stratal OT * Adam Baker University of Arizona tabaker@u.arizona.edu 1.0. Introduction The model of Stratal OT presented by Kiparsky (forthcoming), has not and will not prove uncontroversial

More information

This scope and sequence assumes 160 days for instruction, divided among 15 units.

This scope and sequence assumes 160 days for instruction, divided among 15 units. In previous grades, students learned strategies for multiplication and division, developed understanding of structure of the place value system, and applied understanding of fractions to addition and subtraction

More information

Abstractions and the Brain

Abstractions and the Brain Abstractions and the Brain Brian D. Josephson Department of Physics, University of Cambridge Cavendish Lab. Madingley Road Cambridge, UK. CB3 OHE bdj10@cam.ac.uk http://www.tcm.phy.cam.ac.uk/~bdj10 ABSTRACT

More information

Designing a Computer to Play Nim: A Mini-Capstone Project in Digital Design I

Designing a Computer to Play Nim: A Mini-Capstone Project in Digital Design I Session 1793 Designing a Computer to Play Nim: A Mini-Capstone Project in Digital Design I John Greco, Ph.D. Department of Electrical and Computer Engineering Lafayette College Easton, PA 18042 Abstract

More information

Aspectual Classes of Verb Phrases

Aspectual Classes of Verb Phrases Aspectual Classes of Verb Phrases Current understanding of verb meanings (from Predicate Logic): verbs combine with their arguments to yield the truth conditions of a sentence. With such an understanding

More information

Intensive English Program Southwest College

Intensive English Program Southwest College Intensive English Program Southwest College ESOL 0352 Advanced Intermediate Grammar for Foreign Speakers CRN 55661-- Summer 2015 Gulfton Center Room 114 11:00 2:45 Mon. Fri. 3 hours lecture / 2 hours lab

More information

MAT 122 Intermediate Algebra Syllabus Summer 2016

MAT 122 Intermediate Algebra Syllabus Summer 2016 Instructor: Gary Adams Office: None (I am adjunct faculty) Phone: None Email: gary.adams@scottsdalecc.edu Office Hours: None CLASS TIME and LOCATION: Title Section Days Time Location Campus MAT122 12562

More information

Language Acquisition Fall 2010/Winter Lexical Categories. Afra Alishahi, Heiner Drenhaus

Language Acquisition Fall 2010/Winter Lexical Categories. Afra Alishahi, Heiner Drenhaus Language Acquisition Fall 2010/Winter 2011 Lexical Categories Afra Alishahi, Heiner Drenhaus Computational Linguistics and Phonetics Saarland University Children s Sensitivity to Lexical Categories Look,

More information

TU-E2090 Research Assignment in Operations Management and Services

TU-E2090 Research Assignment in Operations Management and Services Aalto University School of Science Operations and Service Management TU-E2090 Research Assignment in Operations Management and Services Version 2016-08-29 COURSE INSTRUCTOR: OFFICE HOURS: CONTACT: Saara

More information

Approaches to control phenomena handout Obligatory control and morphological case: Icelandic and Basque

Approaches to control phenomena handout Obligatory control and morphological case: Icelandic and Basque Approaches to control phenomena handout 6 5.4 Obligatory control and morphological case: Icelandic and Basque Icelandinc quirky case (displaying properties of both structural and inherent case: lexically

More information

Grading Policy/Evaluation: The grades will be counted in the following way: Quizzes 30% Tests 40% Final Exam: 30%

Grading Policy/Evaluation: The grades will be counted in the following way: Quizzes 30% Tests 40% Final Exam: 30% COURSE SYLLABUS FALL 2010 MATH 0408 INTERMEDIATE ALGEBRA Course # 0408.06 Course Schedule/Location: TT 09:35 11:40, A-228 Instructor: Dr. Calin Agut, Office: J-202, Department of Mathematics, Brazosport

More information

STA 225: Introductory Statistics (CT)

STA 225: Introductory Statistics (CT) Marshall University College of Science Mathematics Department STA 225: Introductory Statistics (CT) Course catalog description A critical thinking course in applied statistical reasoning covering basic

More information

a) analyse sentences, so you know what s going on and how to use that information to help you find the answer.

a) analyse sentences, so you know what s going on and how to use that information to help you find the answer. Tip Sheet I m going to show you how to deal with ten of the most typical aspects of English grammar that are tested on the CAE Use of English paper, part 4. Of course, there are many other grammar points

More information

Ohio s Learning Standards-Clear Learning Targets

Ohio s Learning Standards-Clear Learning Targets Ohio s Learning Standards-Clear Learning Targets Math Grade 1 Use addition and subtraction within 20 to solve word problems involving situations of 1.OA.1 adding to, taking from, putting together, taking

More information

arxiv: v1 [math.at] 10 Jan 2016

arxiv: v1 [math.at] 10 Jan 2016 THE ALGEBRAIC ATIYAH-HIRZEBRUCH SPECTRAL SEQUENCE OF REAL PROJECTIVE SPECTRA arxiv:1601.02185v1 [math.at] 10 Jan 2016 GUOZHEN WANG AND ZHOULI XU Abstract. In this note, we use Curtis s algorithm and the

More information

Navigating the PhD Options in CMS

Navigating the PhD Options in CMS Navigating the PhD Options in CMS This document gives an overview of the typical student path through the four Ph.D. programs in the CMS department ACM, CDS, CS, and CMS. Note that it is not a replacement

More information

Enhancing Unlexicalized Parsing Performance using a Wide Coverage Lexicon, Fuzzy Tag-set Mapping, and EM-HMM-based Lexical Probabilities

Enhancing Unlexicalized Parsing Performance using a Wide Coverage Lexicon, Fuzzy Tag-set Mapping, and EM-HMM-based Lexical Probabilities Enhancing Unlexicalized Parsing Performance using a Wide Coverage Lexicon, Fuzzy Tag-set Mapping, and EM-HMM-based Lexical Probabilities Yoav Goldberg Reut Tsarfaty Meni Adler Michael Elhadad Ben Gurion

More information

We are strong in research and particularly noted in software engineering, information security and privacy, and humane gaming.

We are strong in research and particularly noted in software engineering, information security and privacy, and humane gaming. Computer Science 1 COMPUTER SCIENCE Office: Department of Computer Science, ECS, Suite 379 Mail Code: 2155 E Wesley Avenue, Denver, CO 80208 Phone: 303-871-2458 Email: info@cs.du.edu Web Site: Computer

More information

Page 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified

Page 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General Grade(s): None specified Unit: Creating a Community of Mathematical Thinkers Timeline: Week 1 The purpose of the Establishing a Community

More information

Characteristics of Functions

Characteristics of Functions Characteristics of Functions Unit: 01 Lesson: 01 Suggested Duration: 10 days Lesson Synopsis Students will collect and organize data using various representations. They will identify the characteristics

More information

have to be modeled) or isolated words. Output of the system is a grapheme-tophoneme conversion system which takes as its input the spelling of words,

have to be modeled) or isolated words. Output of the system is a grapheme-tophoneme conversion system which takes as its input the spelling of words, A Language-Independent, Data-Oriented Architecture for Grapheme-to-Phoneme Conversion Walter Daelemans and Antal van den Bosch Proceedings ESCA-IEEE speech synthesis conference, New York, September 1994

More information

Lecture 1.1: What is a group?

Lecture 1.1: What is a group? Lecture 1.1: What is a group? Matthew Macauley Department of Mathematical Sciences Clemson University http://www.math.clemson.edu/~macaule/ Math 4120, Modern Algebra M. Macauley (Clemson) Lecture 1.1:

More information

Mathematics Success Level E

Mathematics Success Level E T403 [OBJECTIVE] The student will generate two patterns given two rules and identify the relationship between corresponding terms, generate ordered pairs, and graph the ordered pairs on a coordinate plane.

More information

Course Syllabus Advanced-Intermediate Grammar ESOL 0352

Course Syllabus Advanced-Intermediate Grammar ESOL 0352 Semester with Course Reference Number (CRN) Course Syllabus Advanced-Intermediate Grammar ESOL 0352 Fall 2016 CRN: (10332) Instructor contact information (phone number and email address) Office Location

More information

Grade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand

Grade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand Grade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand Texas Essential Knowledge and Skills (TEKS): (2.1) Number, operation, and quantitative reasoning. The student

More information

Math 098 Intermediate Algebra Spring 2018

Math 098 Intermediate Algebra Spring 2018 Math 098 Intermediate Algebra Spring 2018 Dept. of Mathematics Instructor's Name: Office Location: Office Hours: Office Phone: E-mail: MyMathLab Course ID: Course Description This course expands on the

More information

Physics 270: Experimental Physics

Physics 270: Experimental Physics 2017 edition Lab Manual Physics 270 3 Physics 270: Experimental Physics Lecture: Lab: Instructor: Office: Email: Tuesdays, 2 3:50 PM Thursdays, 2 4:50 PM Dr. Uttam Manna 313C Moulton Hall umanna@ilstu.edu

More information

Parsing of part-of-speech tagged Assamese Texts

Parsing of part-of-speech tagged Assamese Texts IJCSI International Journal of Computer Science Issues, Vol. 6, No. 1, 2009 ISSN (Online): 1694-0784 ISSN (Print): 1694-0814 28 Parsing of part-of-speech tagged Assamese Texts Mirzanur Rahman 1, Sufal

More information

Course Content Concepts

Course Content Concepts CS 1371 SYLLABUS, Fall, 2017 Revised 8/6/17 Computing for Engineers Course Content Concepts The students will be expected to be familiar with the following concepts, either by writing code to solve problems,

More information