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Course Description form
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Course Title
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English Code /No
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ARABIC code/no.
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credits
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Th.
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Pr.
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Tr.
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TCH
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Fundamentals of Mathematics
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MATH251
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MATH251
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3
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-
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-
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3
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Pre-requisites
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Math110
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Brief contents, to be posted in university site and documents(4-5 lines):
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Basic set theory – Logic - Methods of mathematical proofs - Basic number theory -Complex number system - Mathematical Proofs - Different Types of Proofs -Mathematical Induction - Algebraic Structures - Binary Operations – Group - Ring – Field - Boolean Algebra - Boolean Functions - Representing Boolean Functions.
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Faculties and departments requiring this course (if any): Faculty of science.
Objectives: Prefer In points
1- To know how to think logically and mathematically.
2- To know mathematical arguments.
3- To gain the knowledge of writing proofs
4- To formulate mathematical arguments in an elementary mathematical setting.
5- To know a particular set of mathematical facts of Set theory, Number theory, Complex number system and Algebraic structure and how to apply them.
6- To form a foundation of abstract mathematics
Contents:
1. Logic
1.1 Propositional logic
1.2 Propositional Equivalence
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
2. Basic Structures
2.1 Sets
2.2 Set operations
2.3 Functions
2.4 Sequence and summations
3. Basic Number Theory
3.1 The integers and Division
3.2 Primes and Greatest Common Devisors
3.3 Applications of Number Theory
4. The Complex Number System
4.1 The complex Numbers
4.2 Algebraic properties of C
5 Relations
5.1 Relations and Their Properties
5.2 Representing Relations using Matrices
5.3 Equivalence Relation and Equivalence Classes
5.4 Partial Orderings
6 Mathematical Proofs
6.1 Different Types of Proofs
6.2 Mathematical Induction
7 Algebraic Structures
7.1 Binary Operations
7.2 Group, Ring and Field
8 Boolean Algebra
8.1 Boolean Functions
8.2 Representing Boolean Functions
Course Outcomes:
A- Knowledge:
Students will learn a particular set of mathematical facts and how to apply them; more importantly, from this course students will learn how to think logically and mathematically.
B-Cognitive Skills:
Mental skills, Knowledge, Analysis, Comprehension, Applications and Evaluation
C- Interpersonal skills and responsibilities:
- questioning during lecture
- submitting assignments etc
- group discussions
- understand and response the questions
- communicate effectively
D- Analysis and communication:
)communication, mathematical and IT skills)
Assessment methods for the above elements
Quizzes, Assignments, and Examinations
Text book:
Kenneth. H. Rosen.
Discrete Mathematics and its Applications,
6th Edition . McGraw-Hill, 2007.
Supplementary references
Robert. S. Wolf
Proof, Logic and Conjecture,
W.H. Freeman and Company, New York, 1998
Neville Dean
Discrete Mathematics
Prentice Hall Europe, 1997
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Time table for distributing Theoretical course contents
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Remarks
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Theory
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weak
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Propositional logic(Propositions, Compound propositions, Truth table, Connectives, Conditional and Biconditional, Truth tables of compound propositions, Precedence of logical operators, Translating English sentences)
Propositional Equivalence (Tautology and Contradiction, Logical equivalence, Constructing new logical equivalences)
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1
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Predicates and Quantifiers, Nested Quantifiers(The order of quantifiers, Translating mathematical statements into involving nested quantifiers Translating from nested quantifiers into English)
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2
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Sets(Introduction, The power set, Cartesian product)
Set operations(Basic set operations, Set Identities
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3
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Functions Properties of functions, Inverse functions and compositions of functions, Graphs of functions, Some important functions)
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4
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Sequence and summations(Sequences, Summations, Cardinality), The integers and Division(Division, The division algorithm, Modular arithmetic)
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5
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Primes and Greatest Common Devisors
(Primes, The prime number theorem, Greatest common divisor and least common multiples)
Applications of Number Theory
(Some useful results, Linear congruences)
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6
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The complex Numbers
Algebraic properties of C
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7
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Relations and Their Properties
Representing Relations using Matrices
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8
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Equivalence Relation and Equivalence Classes
Partial Orderings
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9
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Different Types of Proofs
Mathematical Induction
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10
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Binary Operations,Groups
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11
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Rings and Field
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12
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Boolean Functions
Representing Boolean Functions
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13
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Final exam.
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