IE-500 Mathematics of Operations Research
Frequency: Fall Terms
Credit: 3
Catalog description: Introduction to methods of proof, sets and functions, metric spaces,
functions on metric spaces, differential and integral equations, fundamentals of linear algebra.
Course Objectives: The main aim of this course is to equip beginning graduate students with
a level of mathematical sophistication that would be necessary to follow the latter courses in
the program. The main focus will be establishing formal mathematical reasoning.
Course Instructor: Nil Şahin
Teaching Asistant: Özge Şafak
MidTerm1:
%25 (30.11.2013 at 17:40)
MidTerm2:
%25 (03.12.2013 at 17:40)
Final Exam:
%30 (05.01.2014 at 15:30)
Homeworks:
%20
Reference Books:
Mathematical Methods of Engineering Analysis- Erhan Çınlar, Robert J. Vanderbei
Principles of Mathematics in Operations Research- Levent Kandiller
Principles of Mathematical Analysis- Walter Rudin
Current Semester Course Home Page: http://nilsahin.bilkent.edu.tr/ie500.html
Week
1
2
18.09.2013
1 Methods of Proof
Language of mathematics, quantifiers
20.09.2013
Mathematical logic,methods of making proofs
25.09.2013
Disproving statements, the wrong methods of proof
2 Sets and Functions
Sets, set operations
Set operations, Cardinality, Power sets
Functions, image, inverse image,injectiveness, surjectiveness
27.09.2013
3
02.10.2013
04.10.2013
Nov 2- 09.10.2013
4
5
6
7
8
Syllabus(IE-500)
Dates
11.10.2013
Bijectiveness, inverse of a function, composition of functions,
sequences, countability
Countability, Real line and some properties, upper/lower bound,
supremum, infimum
Increasing, decreasing, nonincreasing, nondecreasing functions,
extended real number systems, liminf, limsup and limit of a sequence
in real numbers and extended real numbers
Holiday
Holiday
23.10.2013
25.10.2013
Convergence of a sequence, squeeze theorem,Cauchy criterion, series
Series, Cauchy criterion for series, convergence of series, theorems
about convergence
Tests for convergence of series:ratio test, root test
Comparison test, geometric series test, alternating series test, power
series, radius of convergence, absolutely convergence
Rearrangements of series,
2 Metric Spaces
Definition of metric, metric space
30.10.2013
01.11.2013
06.11.2013
08.11.2013
9
10
11
12
13
14
15
13.11.2013
15.11.2013
20.11.2013
22.11.2013
Inner product, norm, relation between inner product norm and
metric, Cauchy Schwarz inequality, distances from points to sets and
from sets to sets, balls
Open sets in metric spaces
Closed sets in metric spaces, closure of a set
27.11.2013
Interior of a set, boundary of a set, convergence in metric spaces
Bounded sets in metric spaces, subsequences, limit points,
completeness
Completeness of Euclidian Spaces, open covers, compactness
29.11.2013
Compactness,cluster points
04.12.2013
Relation between compactness, completeness, compactness in
Euclidian Spaces
3 Functions on Metric Spaces
Continuity
Continuity, continuity and convergence, continuity and compactness
Uniform Continuity
06.12.2013
11.12.2013
13.12.2013
18.12.2013
20.12.2013
25.12.2013
27.12.2013
4 Linear Algebra
Fields, Vector Spaces, Subspace
Subspaces, linear/affine/convex/canonical combinations
Linear span, affine hull, convex hull, cone of a vector space, generator,
spanning set, linearly dependence, independence
Bases
Dimension, coordinates