Course Details

MATHEMATICS FOR OPTIMIZATION

IE601

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Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS Credits
4IE601MATHEMATICS FOR OPTIMIZATION3+0+037,5

Course Details
Language of Instruction English
Level of Course Unit Master's Degree
Department / Program INDUSTRIAL ENGINEERING
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course This course is designed for a beginning graduate student to gain basic mathematical background required to follow the latter courses in the program. More specifically, in this course we will cover Logic, proof techniques, some basic topics from Real Analysis and Linear Algebra with a flavor of establishing formal mathematical reasoning. To do this, the course consists of the following 3 parts:
Part I: Symbolic Logic, and methods of mathematical proofs
Part II: Basic Real Analysis, including Metric Spaces
Part III: Basic Linear Algebra and some topics from Advanced Linear Algebra
In this course, by covering a subject that you might have encountered during your undergraduate calculus or linear algebra courses, we aim to work on them with more in-depth analysis and understanding.
Course Content Symbolic logic, proof methods including the principle of induction, sets and functions, properties of rational, real and complex numbers, countability, Euclidean spaces, properties of R as a metric space, notion of accumulation point, convergence of sequences, metric spaces, basic topological notions such as compactness and connectedness, basic properties of sequences and series, limit, continuity and differentiability, sequences and series of functions, revise of basic linear algebra topics including, properties of vectors, norms, vector spaces, subspaces, bases, linear transformations, eigenvalues and eigenvectors, orthogonality, orthogonal projection, inner product spaces.
Course Methods and Techniques ...
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. Zübeyir Çınkır people.agu.edu.tr/zcinkir/ zubeyir.cinkir@agu.edu.tr
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Kenneth H. Rosen, Discrete Mathematics and its Applications, 6th or newer edition.
Tosun Terzioğlu, An Introduction to Real Analysis.
Mathematical Methods of Engineering Analysis, Erhan Çınlar and Robert J. Vanderbei. http://www.princeton.edu/~rvdb/506book/book.pdf
Linear Algebra and Its Applications, 5th Edition (or new edition). Authors: David C. Lay.
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Course Category
Mathematics and Basic Sciences %100

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Yarıyıl İçi Çalışmalarının Başarı Notunun Katkısı 1 % 30
Quiz/Küçük Sınav 5 % 5
Ödev 10 % 25
Final examination 1 % 40
Total
17
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Yazılı Sınav 1 20 20
Ev Ödevi 10 8 80
Kısa Sınav 5 1 5
Araştırma 5 5 25
Ders dışı çalışma 10 2 20
Derse Devam 15 3 45
Final Sınavı 1 30 30
Total Work Load   Number of ECTS Credits 7,5 225

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Write a mathematical proof by using various proof methods and by using the rules of symbolic logic.
2 Solve basic questions from Calculus topics such as sequences, limits, continuity, differentiability, extreme value theorems by using epsilon-delta definition and proof techniques.
3 Understand the metric structures of real numbers and rational numbers.
4 Develop an understanding of basic concepts of metric spaces, such as accumulation point, openness and closedness, compactness, convergence of sequences, connectedness, continuity of functions.
5 Give proofs of important theorems from basic linear algebra.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Symbolic Logic: Proposition, connectives, rules of logic, analogies with sets and bit operations. Converse, inverse and contrapositive of a proposition. - -
2 Predicates, universal and existential quantifiers, nested quantifiers, and their usage in mathematics such as limit definition, definition of a function, onto and 1-1 functions. - -
3 Proof Methods: Direct proof, indirect proof, conditional proof, proof by contraposition, proof by contradiction, counter example, proof by cases, constructive proofs. - -
4 Principle of mathematical induction. Sets and Functions including properties of big Union and big Intersection , image and pre-image of sets under a function, countable and uncountable sets. Definition of relations and their basic properties: Reflexivity, symmetricity, transitivity and anti-symmetricity. Definition of equivalence and partial order relations. - -
5 Limit, continuity, and differentiation via epsilon-delta definition. - -
6 Real and Complex number systems. Properties of Q (the set of rational numbers) and R (the set of real numbers), Euclidean spaces. Minimum, maximum, infimum and supremum of a set. - -
7 Basic Topology: Metric spaces, open and closed sets, accumulation point. - -
8 Midterm I - -
9 Compact sets, continuity of functions between metric spaces. - -
10 Perpect sets, connected sets. - -
11 Sequences and series: absolute convergence, rearrangement of series. - -
12 Sequence and series of functions. - -
13 Basic Linear Algebra: Vector spaces, subspace, spanning set, linearly dependent and independent vectors, bases of a vector space, linear transformation and matrices. Row, column and null space of a matrix. - -
14 Eigenvalues and eigenvectors, diagonalization. - -
15 Orthogonality, orthogonal projection, Inner product. - -


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
C1 5 5 5 4 4 4
C2 5 4 4 1 1 1
C3 4 3 4 1 1 1
C4 4 3 4 1 1 1
C5 4 3 4 1 1 1

Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant


https://sis.agu.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=75506&lang=en
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