Toplu Ders İçerikleri

Title of the course: Bilim ve bilimsel gelişmeler
Instructor: Dr. Vedat Tanrıverdi
Institution: ODTÜ
Dates: 9-15 July 2018
Prerequisites: -
Level: Beginning undergraduate
Abstract: 14’üncü yüzyıla kadar bilimsel gelişmelerin kısa bir özeti ile başlanacak Avrupa’da bilimsel gelişmelerin başlama süreci ile devam edilecektir. Bilimin ve bilimsel yöntemin tanımı ve bilimsel etiğin nasıl olması gerektiğine dair konulara değinilecektir.
Language: TR

Title of the course: Group Theory I
Instructor: Asst. Prof. Roghayeh Hafezieh
Institution: Gebze Teknik Üniversitesi
Dates: 9-15 July 2018
Prerequisites: Algebra I
Level: Undergraduate
Abstract: In group theory I, we will discuss: "The notion of a group, subgroup, cosets, Cyclic groups, generators, normal subgroups, Isomorphism laws, conjugation, permutations, symmetric group and alternating group."
Language: EN

Title of the course: Linear Algebra and Its Applications
Instructor: Asst. Prof. Seyfi Türkelli
Institution: Western Illinois University
Dates: 9-15 July 2018
Prerequisites: -
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: This is a one-week course on Linear Algebra and Its Applications. In this class, we will see:
Vectors and Operations on Vectors
Matrices and Operations on Matrices
Linear Systems, Elementary Row Operations on Matrices, Gauss-Jordan Elimination Method
Vector Spaces and Subspaces
Examples of Subspaces
GPS Systems
Language: EN

Title of the course: Introduction to Ring Theory
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 9-15 July 2018
Prerequisites: -
Level: Undergraduate, advanced undergraduate, graduate.
Abstract:
1. What is a Ring? 
2. Factorization in Polynomial Rings 
3. Ideals, Homomorphisms and Factor Rings
4. Unique Factorization Domains 
5. Further Topics in Ring Theory
Language: TR, EN

Title of the course: Sonlu Grupların Temsilleri
Instructor: Assoc. Kağan Kurşungöz
Institution: Sabancı Üniversitesi
Dates: 9-15 July 2018
Prerequisites: lineer cebir, lisans seviyesinde soyut cebir.
Level: Lisans 3-4 ve yüksek lisans öğrencileri
Abstract: Temel kavramlar, matris temsilleri, G-modülleri ve grup cebiri, indirgenebilme, G-homomorfizmaları, grup karakterleri, grup cebirinin ayrışımı, indirgenmiş temsiller.
Kaynak kitap: The Symmetric Group (Bruce Sagan)
Language: Türkçe

Title of the course: A quick course in knot theory
Instructor: Dr. Neslihan Güğümcü
Institution: National Technical University of Athens
Dates: 9-15 July 2018
Prerequisites: -
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: Knots have been objects of mathematics since the 18th century. Today the theory of knots is a developed theory lying in the branch of algebraic topology and it interrelates with many other areas such as mathematical physics, physics, biology and chemistry. In this course, we will learn the basics of the theory of knots. The outline of the course will be mostly as follows.
Day 1: Basic concepts of  algebraic & geometric topology
Day 2: Knots and links in mathematics: an overview discussion and formal definitions and basic theorems
Day 3: Simple invariants of knots and links
Day 4: Some polynomial invariants of knots and links
Day 5: The Jones polynomial and the Kauffman bracket
Day 6: Other knotted objects; An introduction to the theory of braids and tangles,  Applications of the knot theory to biology, physics and chemistry
Language: TR, EN

Title of the course: Elementary Algebraic Geometry
Instructor: Dr. Christian Urech
Institution: Imperial College
Dates: 9-15 July 2018
Prerequisites: Linear algebra, basic commutative algebra such as rings, ideals etc.
Level: Advanced undergraduate, graduate
Abstract: The aim is to give a very gentle and elementary introduction to algebraic geometry. I will try to cover the following subjects: Noetherian rings, Zariski topology, Hilbert Nullstellensatz, affine varieties and their coordinate rings, morphisms between varieties.
Language: EN

Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Ü.
Tarih: 9-22 Temmuz 2018
Dersin Adı: Simetriler
İçerik: Konumuz matematiksel yapıları koruyan dönüşümler olacak. Daha çok klasik sayı kümelerine, çizgelere, geometrik şekillere odaklanacağız. Çok boyutlu uzaylara da geçeceğiz, örneğin n boyutlu küplerin simetrilerini bulacağız.

Eğitmen: MSc. Kübra Dölaslan
Kurum: ODTÜ
Tarih: 9-22 Temmuz 2018
Dersin Adı: Problem Saati
İçerik: Bu derste, gün boyunca işlenen konularla ilgili problemler çözülecek, öğrencilerin soruları yanıtlanacaktır. Not: Problemler kolay olmayacaktır ve öğrenciden aktif katılım beklenecektir.

Eğitmen: Prof. Yusuf Ünlü
Kurum: Yeditepe Ü.
Tarih: 9-22 Temmuz 2018
Dersin Adı: Polinomlar
İçerik: Bölme algoritması, Cebirsel türev, Bézout Teoremi, esas ideal bölgeleri, Tek türlü çarpnalara ayrılabilme bölgeleri, simetrik polinomlar.

Eğitmen: Doç. Dr. Kağan Kurşungöz
Kurum: Sabancı Ü.
Tarih: 9-22 Temmuz 2018
Dersin Adı: Soyut Cebir
İçerik: Temel bilgiler (kümeler, bağıntı, fonksiyon, işlem, tam sayılar, modüler aritmetik), gruplar (grubun tanımı, devirli grup, alt grup, eşküme(koset), normal alt grup, permütasyon grupları, abelyen gruplar), homomorfizmalar, grup etkileri, (vakit kalırsa) halka ve cisimler.
Kullanabilecek kaynaklar: Elements of Abstract Algebra (Allan Clark), A first course in abstract algebra (John B. Fraleigh), Örneklerle Soyut Cebir (Prof. Dr. Fethi Çallıalp)

Title of the course: Examples in Group Theory
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 9-22 July 2018
Prerequisites: None
Level: Undergraduate, advanced undergraduate, graduate.
Abstract: We will give lots of examples of groups and prove and apply the theorems on these examples.
Language: TR, EN

Title of the course: Topolojiye Giriş
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 9-22 July 2018
Prerequisites: Temel kümeler kuramı.
Level: Her seviye.
Abstract: Açık ve kapalı kümeler ve komşuluk. Kapanış ve iç kavramları. Hausdorff uzayları. Sürekli fonksiyonlar. Topoloji üretmek. Kartezyen topoloji. Topolojinin kısıtlanması. Metrik uzaylar. Ultrametrik. Tıkız kümeler. Tychonoff teoremi.
Language: EN, TR

Title of the course: Temel türevli (differential) denklemlerin fizikte kullanımı
Instructor: Dr. Vedat Tanrıverdi
Institution: ODTÜ
Dates: 16-22 July 2018
Prerequisites: -
Level: Beginning undergraduate
Abstract: Türev ve integralin temel tanımı, Newton’un ikinci yasası, kütleçekim yasası, harmonik hareket, dalga hareketi.
Language: TR

Title of the course: Group Theory II
Instructor: Asst. Prof. Roghayeh Hafezieh
Institution: Gebze Teknik Üniversitesi
Dates: 16-22 July 2018
Prerequisites: Algebra I
Level: Graduate and advanced undergraduate
Abstract: In group theory II, we will discuss: "Elementray results on group theory, Direct product, Group action, Cayley theorem, Sylow theorems and their proofs, application of sylow theorems, simple groups, some classification."
Language: EN

Title of the course: Leibniz Cebirlerine Giriş
Instructor: Asst. Prof. Nil Mansuroğlu
Institution: Ahi Evran Üniversitesi
Dates: 16-22 July 2018
Prerequisites: -
Level: Graduate, advanced undergraduate
Abstract:
1. Day : Lie cebirlerine giriş
2. Day: Leibniz cebirlerinin temel kavramları
3. Day: Leibniz cebirleri ile ilgili örnekler
4. Day: -
5. Day: Yapı sabitleri
6. Day: 1, 2, 3 boyutlu Leibniz cebirleri

7. Day: Nilpotent Leibniz cebirleri
Language: TR

Title of the course: Introduction to Field Theory
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 16-22 July 2018
Prerequisites: Linear Algebra
Level: Advanced undergraduate, graduate.
Abstract: Field extensions, algebraic extensions, automorphisms of fields, finite fields.
Language: TR, EN

Title of the course: Young Tabloları
Instructor: Assoc. Kağan Kurşungöz
Institution: Sabancı Üniversitesi
Dates: 16-22 July 2018
Prerequisites: Lisans cebirine biraz göz aşinalığı
Level: Lisans 3-4 ve yüksek lisans öğrencileri
Abstract: Young tablolarında muhtelif işlemler, kelimeler üzerinde işlemler, Robinson-Schensted-Knuth eşlemesi, (vakit kalırsa) simetrik polinomlar.
Kaynak Kitap: Young Tableaux (William Fulton)
Language: Türkçe

Title of the course: Geometric group theory
Instructor: Dr. Christian Urech
Institution: Imperial College
Dates: 16-22 July 2018
Prerequisites: Basic notions in group theory (normal subgroups, quotients, isomorphism theorems etc.)
Level: Advanced undergraduate, graduate
Abstract: Generators and relations, free groups, graphs, Cayley graphs, group actions, trees, Nielsen Schreier theorem.
Language: EN

Title of the course: Group Actions and Sylow Theory
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 23-29 July 2018
Prerequisites: Basic group theory
Level: Advanced undergraduate, graduate.
Abstract: Our purpose will be to prove Sylow Theorems and to give some of their applications.
Language: TR, EN

Title of the course: Finite Fields
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 23-29 July 2018
Prerequisites: -
Level: Advanced undergraduate, graduate.
Abstract: Finite fields: existence, uniqueness, structure, explicit construction. Frobenius automorphisms. Galois’s Theory of finite fields.
Language: TR, EN

Title of the course: Elektromanyetik teoriye giriş
Instructor: Dr. Vedat Tanrıverdi
Institution: ODTÜ
Dates: 23-30 July 2018
Prerequisites: Temel differansiyel ve integral kavramları, temel elektrostatik bilgi
Level: Advanced undergraduate
Abstract: Coulumb yasası ile başlayıp Maxwell denklemlerinin differansiyel haline kadar işlenecektir.
Language: TR

Title of the course: Elements of Matrix Algebra
Instructor: Prof. Alexandre Borovik
Institution: Manchester U.
Dates: 23 -29 July 2018
Prerequisites: School level algebra
Level: Younger undergraduate students and fresh school leavers
Abstract: Entry level course which will focus on two topics usually not discussed in standard undergraduate courses:
What is reduced echelon form of matrix, really? What is its meaning and what it is doing?
What is the rank of a matrix?
Language: English

Title of the course: p-adic numbers and power series
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 23-30 July 2018
Prerequisites: Basic facts about modular numbers and polynomials.
Level: All
Abstract: The ring of polynomials and power series. The use of power series in counting. Different construction of p-adic numbers. Hensel's Lemma. Ultrametric and completion of rings.
Language: EN, TR

Title of the course: Examples of Automorphism Groups
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 23-29 July 2018
Prerequisites: TBA
Level: Undergraduate, advanced undergraduate, graduate
Abstract: TBA
Language: EN, TR

Title of the course: Introduction to Manifolds with Special Holonomy
Instructor: Dr. Özgür Kelekçi
Institution: Türk Hava Kurumu Ü.
Dates: 23-29 July 2018
Prerequisites: Basic Differential Geometry (not a must but preferable).
Level: Graduate, advanced undergraduate
Abstract: Manifolds with special holonomy attract significant interest in both mathematics and mathematical physics. They appear in many contexts in Riemannian geometry, particularly Ricci-flat and Einstein geometry, minimal submanifold theory and the theory of calibrations, and string theory. We will start with basics of Riemannian geometry. The emphasis will be on discussing the Ricci-flat geometries that occur, then the holonomy classifications will be studied.
Language: EN

Title of the course: Finans Matematiği
Instructor: Assoc. Prof. Deniz Ünal
Institution: Çukurova Ü.
Dates: 23-30 July 2018
Prerequisites: -
Level: Advanced undergraduate, beginning undergraduate
Abstract:
Temel kavramlar, basit/bileşik faiz-iskonto
Eşdeğer Senetler
Dış/iç İskonto
Ani Faiz
Paranın bugünkü/gelecekteki değeri
Annüiteler (düzenli ödemeli, değişken ödemeli, sonlu/sonsuz, sürekli ödemeli)
Language:
TR

Title of the course: Lie algebras
Instructor: Assoc. Prof. Şükrü Yalçınkaya
Institution: İstanbul Ü.
Dates: 23 July - 5 August 2018
Prerequisites: Good knowledge on linear algebra
Level: Advanced undergraduate, graduate
Abstract: Definitions and examples. Solvable and nilpotent Lie algebras. Semisimple Lie algebras. Root systems of semisimple Lie algebras.
Language: Turkish, English

Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Ü.
Tarih: 23 Temmuz – 5 Ağustos 2018
Dersin Adı: Gerçel Sayılar Yapısı
İçerik: Gerçel sayılar aksiyomatik olarak tanımlayıp, "Arşimet Özelliği" ve "tamlık" gibi gerçel sayıların en temel özelliklerini kanıtlayacağız. Bunu yapmak için Cauchy dizilerini ve yakınsak dizileri tanımlamalıyız. Bu klasik konulardan sonra gerçel sayıların biricikliğini tartışacağız. Son günlerde sonsuz küçük elemanların olduğu ve gerçel sayılara çok benzeyen yapılar tanımlayacağız.

Eğitmen: Doç. Dr. Özlem Beyarslan
Kurum: Boğaziçi Ü.
Tarih: 23 Temmuz – 5 Ağustos 2018
Dersin Adı: Diziler ve seriler
İçerik: 1. Gerçel sayıların özellikleri 2. yakınsak gerçel sayı dizileri 3. Limitin biricikliği 4.Yakınsak dizilerle işlemler 5. Monoton diziler 6. Cauchy dizileri 7. Gerçel sayıların tamlığı 8. Bolzano Weierstrass teoremi 9. Seriler 10. Serilerde yakınsaklık  11. Kıyaslama teoremleri 12. Yakınsaklık testleri

Eğitmen: Yard. Doç. Saadet Özer
Kurum: İstanbul Bilgi Ü.
Tarih: 23 Temmuz – 5 Ağustos 2018
Dersin Adı: Kalkülüs
İçerik: Fonksiyonlar, Limit, Süreklilik, Türev, Türevin Uygulamaları, İntegral ve uygulamaları.

Eğitmen: MSc. Kübra Dölaslan
Kurum: ODTÜ
Tarih: 23 Temmuz – 5 Ağustos 2018
Dersin Adı: Problem Saati
İçerik: Bu derste, gün boyunca işlenen konularla ilgili problemler çözülecek, öğrencilerin soruları yanıtlanacaktır. Not: Problemler kolay olmayacaktır ve öğrenciden aktif katılım beklenecektir.

Title of the course: An introduction to social choice theory
Instructor: Prof. Remzi Sanver
Institution: CNRS, Universite Paris Dauphine
Dates: 30 July – 5 August 2018
Prerequisites: Temel mantık kavramlarına aşina olmak.
Level: Graduate ile advanced undergraduate arası
Abstract: The course introduces basic concepts and results of the theory of decision making, including May’s characterization of majoritarianism and Arrow’s impossibility theorem.
Language: EN, TR

Title of the course: Fractal dimensions in Analysis
Instructor: Asst. Prof. Kemal Ilgar Eroğlu
Institution: İstanbul Bilgi Ü.
Dates: 30 July – 5 August 2018
Prerequisites: Undergraduate-level measure theory is recommended.
Level: Graduate, advanced undergraduate
Abstract: In this course we will go over various kinds of (fractal) dimensions that are used in analysis and study their elementary properties.
Language: TR, EN

Title of the course: Introduction to Ring Theory
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 30 July – 5 August 2018
Prerequisites: None
Level: Undergraduate, advanced undergraduate, graduate.
Abstract: Definition and examples of rings. Subrings. Ideals. Ideals generated by a subset. Quotient ring. Fundamental theorem of ring theory. Chinese remainder theorem.
Language: TR, EN

Title of the course: Topics in Polynomials
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 30 July – 5 August 2018
Prerequisites: TBA
Level: Undergraduate, advanced undergraduate, graduate
Abstract: TBA
Language: TR, EN

Title of the course: Galois Theory
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 30 July – 5 August 2018
Prerequisites: -
Level: Advanced undergraduate, graduate.
Abstract: Field extensions. Minimal polynomial. Construction of simple algebraic extension from an irreducible polynomial. The field of algebraic numbers. Splitting field,  Normal and separable extensions, Fundamental theorem of Galois Theory.
Language: TR, EN

Title of the course: q-series and applications to number theory
Instructor: Prof. Mehmet Cenkci
Institution: Akdeniz Ü.
Dates: 30 July – 5 August 2018
Prerequisites: Mathematical analysis
Level: Undergraduate, graduate
Abstract: q-series and theta functions, Fundamental theorems about q-series and theta functions, Sums of squares and triangular numbers, Congruences for partition function.
Language: TR, EN

Title of the course: "Down with determinants!"
Instructor: Prof. Alexandre Borovik
Institution: Manchester U.
Dates: 30 July - 5 August 2018
Prerequisites: Basics of linear algebra (for example, my course the previous week, or any linear algebra course in any university)
Level: Younger undergraduate students
Abstract: A chapter in linear algebra: eigenvalues and eigenvectors explained without mentioning determinants. The lectures will be based on the famous paper by Sheldon Axler, "Down with determinants!". American Mathematical Monthly 102 (1995), 139-154 (available at http://www.axler.net/DwD.html). However, I will be working with matrices rather than linear transformations.
Language: English

Title of the course: Basic knot theory
Instructor: Dr. Georgios Dimitroglou Rizell
Institution: Uppsala University
Dates: 30 July – 5 August 2018
Prerequisites: Calculus. Elementary group theory and elementary topology are very helpful, but not required.
Level: Graduate, advanced undergraduate, beginning Undergraduate
Abstract: This is a beginners course on knot theory in three dimensions. We will study classical toplogical notions such as linking numbers, Seifert surfaces, and the knot group. In addition we will introduce certain knot polynomials (e.g. the Alexander, Jones, and A-polynomials), which are more modern invariants of knots.
Language: EN

Title of the course: Ayrık Matematik
Instructor: Asst. Prof. Ayhan Dil
Institution: Akdeniz Ü.
Dates: 30 July -  12 August 2018
Prerequisites: Calculus
Level: Undergraduate (1-2)
Abstract:
Recurrent Problems
Sums
Integer Functions
Number Theory
Binomial Coefficients
Special Numbers
Generating Functions
Language: TR

Eğitmen: Prof. Haluk Oral
Kurum: -
Tarih: 6-12 Ağustos 2018
Dersin Adı: Matematik Sohbetleri
İçerik: Sayma problemleri, reel sayıların bazı özellikleri, Binom teoremi, Öklid algoritması, şifreleme.

Eğitmen: Prof. Melih Boral
Kurum: -
Tarih: 6-12 Ağustos 2018
Dersin Adı: Sayılar Kuramı
İçerik: Tamsayıların özellikleri, kongruens, Fermat ve Euler teoremleri, lineer kongruensler, kuadratik residüler.

Eğitmen: Prof. Melih Boral
Kurum: -
Tarih: 6-12 Ağustos 2018
Dersin Adı: Sayılar Kuramı
İçerik: Tamsayıların özellikleri, kongruens, Fermat ve Euler teoremleri, lineer kongruensler, kuadratik residüler.

Title of the course: Elliptic curves
Instructor: Dr. Dino Festi
Institution: JGU Mainz
Dates: 6-12 August 2018
Prerequisites: Basic commutative algebra and analysis
Level: Graduate, advanced undergraduate
Abstract: This course is meant to be an introduction to the study of elliptic curves. We will approach the subject from both an algebraic point of view and a complex analytic one. The final goal of the course is to show that the categories of complex tori, lattice of rank 2, and elliptic curves over the complex field are equivalent. More details can be find in the syllabus of the course given last year (see attachment).
Textbook or/and course webpage:
Silverman, `the arithmetic of elliptic curves’.
Course’s notes (see attachment).
Language: EN

Title of the course: Algebraic Curves
Instructor: Dr. Davide Cesare Veniani
Institution: Johannes Gutenberg-Universität Mainz
Dates: 6-12 August 2018
Prerequisites: Basic ring theory (ideals, polynomials, fields, algebraic closure)
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: This course is intended as an invitation to algebraic geometry. The theory of algebraic curves already shows many of the complexities of this field, but it is an accessible topic that will help the students build a strong intuition. The main focus will be on affine and projective plane curves, but we will also develop fundamental algebraic tools such as Hilbert’s Nullstellensatz and discrete valuation rings. Our main result will be Bézout’s Theorem. This course will be a complement to Dino Festi’s course on elliptic curves.
Textbook or/and course webpage: “Algebraic Curves” by W. Fulton, chapters 1-5
(http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf)
Language: EN

Title of the course: Topics in algebraic number theory
Instructor: Dr. Pınar Kılıçer
Institution: Oldenburg University
Dates: 6-12 August 2018
Prerequisites: Basic algebra, linear algera, field theory, module theory.
Level: Graduate, advanced undergraduate
Abstract:
- Number rings, ideals in number rings
- Explicit ideal factorization in number rings
- Geometry of numbers and applications
- Computing units and class groups
Textbook or/and course webpage: Daniel A. Marcus – Number Fields
Language: EN

Title of the course: Bernoulli Numbers and Zeta Functions
Instructor: Prof. Mehmet Cenkci
Institution: Akdeniz Ü.
Dates: 6-12 August 2018
Prerequisites: Basic complex analysis including residue theorem and analytic continuation.
Level: Undergraduate, graduate
Abstract: Bernoulli numbers; Stirling numbers; Clausen and von Staudt Theorem and Kummer’s Congruence; Generalized Bernoulli numbers; The Euler-Maclaurin Summation Formula and the Riemann zeta function; Special values and complex integral representation of L-functions.
Language: TR, EN

Title of the course: Stochastic Optimization
Instructor: Dr. Tatiana González Grandón
Institution: Humboldt Universität Berlin
Dates: 6-12 August 2018
Prerequisites: Linear Optimization
Level: Graduate, advanced undergraduate
Abstract: Stochastic optimization refers to a collection of methods for minimizing/maximizing an objective function when randomness is present. We will study the types of problems when uncertainty is present in the constraint functions. Over the last few decades these methods have become essential tools for economics, engineering, business and computer science. We will look at applications and essential theory to solve this type of problems.
1. Optimization with random variables Introduction to Optimization Problems with uncertainties and to Probability Tools.
2. Probability Constraints Examples and Solutions.
3. Continuity & Differentiability of Probability Constraints
4. When do we have convexity? Prékopa's Theorem
5. Numerical Solutions and Discussion of Optimization Examples.
Textbook or/and course webpage:
1. Stochastic Programming. Andras Prékopa.
2. Lectures on Stochastic Programming (Modeling and Theory). A. Shapiro, D. Dentcheva.
Language: EN

Title of the course: Modular Forms and L functions in Analytic Number Theory
Instructor: Dr. Eren Mehmet Kıral
Institution: -
Dates: 6-12 August 2018
Prerequisites: Complex Analysis, Fourier analysis.
Level: Graduate, advanced undergraduate
Abstract:
Day 1: The Gauss Circle Problem, Voronoi Summation formula
Day 2: The jacobi theta function, every number can be written as a sum of four squares.
Day 3: The Riemann Zeta function, Riemann's memoir (a proof of Prime number theorem if Riemann Hypothesis were true)
Day 4: Kloosterman's original paper on representing integers by quadratic forms in four variables where a Kloosterman sum is first introduced
Day 5: Modular forms on the upper half plane, (for those also taking the Elliptic curve class) what did Andrew Wiles' modularity theorem which led to a proof of Fermat's Last Theorem actually say (no proof).
Day 6: Eisenstein series, Poincare series, Petersson Trace formula (more Kloosterman sums!). (Or some other topic you might ask during the week, but give me early notice)
Language: TR, EN

Title of the course: Quadratic Forms and the Hasse-Minkowski Theorem
Instructor: Dr. Martin Djukanovic
Institution: Ulm University
Dates: 6-12 August 2018
Prerequisites: Basic algebra, basic analysis helps but is not necessary.
Level: Graduate, advanced undergraduate
Abstract: We introduce the concept of a Diophantine equation, with some classical results and examples (Pythagorean triples, theorems of Fermat and Legendre). We prove the Quadratic Reciprocity Law, introduce p-adic numbers and Hensel's Lemma (without a formal proof), and we prove the basic properties of the Hilbert symbol. Finally, if time permits, we state and prove the Hasse-Minkowski theorem for ternary quadratic forms.
Language: EN

Title of the course: Introduction to Quantum Computing
Instructor: Asst. Prof. Ahmet Çevik
Institution: JSGA, ODTÜ
Dates: 6-12 August 2018
Prerequisites: Linear algebra
Level: Graduate and advanced undergraduate   
Abstract: This is a concise introduction course in quantum computing for mathematicians and computer scientists. We aim to cover some fundamental topics in quantum computing such as the mathematical representation of quantum systems, quantum teleportation, superdense coding, some basic quantum algorithms including the Deutsch algorithm, Deutsch-Josza algorithm, Simon’s periodicity algorithm, and quantum models of computation. Only elementary linear algebra is required for this course. We will not assume for the auidiance to have any background on quantum mechanics, though some familiarity would certainly help.
Language: TR, EN

Title of the course: Elementary Number Theory
Instructor: Dr. Cihan Pehlivan
Institution: -
Dates: 6-12 August 2018
Prerequisites: -
Level: Beginning undergraduate
Abstract: Congruences, Chinese Remainder Theorem, Primitive Roots, Quadratic Residues and Reciprocity, Arithmetic Functions, Diophantine Equations.
Primitive roots, quadratic residues and reciprocity, Euler Phi Function.
Language: TR

Title of the course: Topics in Number Theory
Instructor: Dr. Haydar Göral
Institution: Koç Ü.
Dates: 6-19 August 2018
Prerequisites: Calculus
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: The course will be two weeks but each week will be independent from each other.
First week: Prime numbers, sieve methods, zeta functions
Second week: Additive number theory, some special functions and numbers
Language: TR, EN

Eğitmen: Ali Törün
Kurum: -
Tarih: 6-19 Ağustos 2018
Dersin Adı: Meşhur Problemler ve Hikâyeleri
İçerik: Matematik tarihinde yer almış bazı meşhur popüler matematik problemlerinin kısa hikâyesi ve ünlü matematikçilerin bu problemlere getirdikleri çözümlerin incelenmesi.

Eğitmen: MSc. Kübra Dölaslan
Kurum: ODTÜ
Tarih: 6-19 Ağustos 2018
Dersin Adı: Problem Saati
İçerik: Bu derste, gün boyunca işlenen konularla ilgili problemler çözülecek, öğrencilerin soruları yanıtlanacaktır. Not: Problemler kolay olmayacaktır ve öğrenciden aktif katılım beklenecektir.

Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Ü.
Tarih: 13-19 Ağustos 2018
Dersin Adı: Kombinasyon Hesapları ve Olasılık
İçerik: Asıl amacımız olasılık kuramı olacak. Olay kümemiz sonlu ya da sonsuz, ayrık ya da sonsuz olabilecek. Ama çoğu kez olasılık problemlerinde kombinasyon hesapları da gerekir. Kombinasyon hesaplarını ihtiyacımız olduğu kadar inceleyeceğiz. Her gün bir ya da iki probleme odaklanılacak. Öğrencilerin bu derste aktif olmaları beklenmektedir.

Eğitmen: Dr. Tülay Ayyıldız Akoğlu ve Dr. Kemal Akoğlu
Kurum: Karadeniz Teknik Ü.
Tarih: 13-19 Ağustos 2018
Dersin Adı: Algoritmalarla Matematik
İçerik: Bu dersin amacı bir matematik probleminin algoritmalar yoluyla nasıl çözülebileceğini öğretmektir. Dersteki algoritmalar “pseudocode” şeklinde öğretilecek, daha sonra herhangi bir programlama dili ile bilgisayarda uygulama yapabilmesinin altyapısı oluşturulmuş olacaktır. İlk derste algoritma nedir ve matematik bilgisayara nasıl öğretilir, bilgisayar yardımıyla matematik problemleri nasıl çözülebilir soruları cevaplanacaktır.
Bir algoritmanin bileşenleri açıklanacak, kullanılabilecek veri tipleri ve yapıları (for, while, if/ then gibi temel enstrumanlar) tanıtılacaktır.
Daha sonra sıralama ve arama (searching/sorting) algoritmalarından birer örnek verilecektir, bu algoritma sayısal birer örnek ile öğrencilere uygulanacaktır.
Algoritma dizaynı ve uygulaması interaktif şekilde olmak üzere aşağıdaki konular üzerinde çalışılacaktır:
- Bir tam sayının faktoriyelini hesaplama,
- Tam sayıların ebob ve ekoklarını bulma,
- Belirli bir aralıktaki asal sayıları bulma,
- İki şehir arasında en kısa yolu bulma (iki farklı algoritma ile).

Title of the course: Orders of Finite Simple Groups
Instructor: Prof. Ayşe Berkman
Institution: MSGSÜ
Dates: 13-19 August 2018
Prerequisites: Basic knowledge of group theory including Sylow Theorems.
Level: Graduate, advanced undergraduate        
Abstract: This will be more like a workshop centered on the question “Which positive integers are orders of finite simple groups?” I shall teach the necessary concepts, theorems, and techniques of group theory, and students will be assigned to make short presentations at the board.
Language: TR, EN

Title of the course: Numerical Semigroups
Instructor: Prof. Halil İbrahim Karakaş
Institution: Başkent Ü.
Dates: 13-19 August 2018
Prerequisites: Elementary number theory
Level: Graduate, advanced undergraduate
Abstract: Monoids and monoid homomrophisms, Multiplicity and embedding dimension, Frobenius number, genus, conductor and pseudo frobenius numbers, Symmetric and pseudo-symmetric numerical semigroups.
Textbook: J. C. Rosales, P. E. Garcia-Sanchez. Numerical Semigroups, Springer, 2009.
Language: TR, EN

Title of the course: Introduction to Module Theory
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 13-19 August 2018
Prerequisites: Ring theory
Level: Advanced undergraduate, graduate.
Abstract: Definition and examples. Homomorphisms. Fundamental theorem. Linear independence and sets of generateors. Free modules.
Language: TR, EN

Title of the course: Continued fractions
Instructor: Prof. David Pierce
Institution: MSGSÜ
Dates: 13-19 August 2018
Prerequisites: None.  We shall study some topics that may be studied in a second-semester number-theory course; however, no specific results are required from a first-semester course.
Level: Graduate, advanced undergraduate
Abstract: We accept from childhood that multiplication of whole numbers is commutative; but Euclid gives a rigorous proof based on what we now call the Euclidean algorithm.  This algorithm can be used to write any real number as a continued fraction.  The continued fraction repeats when the real number is the solution of a quadratic equation.  This case yields the solutions of a so-called Pell equation, x^2 - dy^2 = 1, an example of a Diophantine equation.
Textbook or/and course webpage: http://mat.msgsu.edu.tr/~dpierce/Courses/Sirince/ (in preparation)
Language: TR; EN

Title of the course: Philosophy of Mathematics
Instructor: Asst. Prof. Ahmet Çevik
Institution: JSGA, ODTÜ
Dates: 13-19 August 2018
Prerequisites: Curiosity
Level: Advanced undergraduate, beginning Undergraduate
Abstract: This is an introductory course in philosophy of mathematics. We will cover some fundamental subjects and various philosophical views concerning the ontology, epistemology and methodology of mathematics, including mathematical realism (Platonism), intuitionism, logicism, and formalism if time permits. No background is assumed, the course will be self-contained.
Textbook or/and course webpage: A. Çevik, Matematik Felsefesi ve Matematiksel Mantık, submitted.
Language: TR, EN

Title of the course: Dış cebire giriş ve Riemann geometrindeki bazı uygulamaları
Instructor: Prof. Dr. Muzaffer Adak
Institution: Pamukkale Üniversitesi
Dates: 13-19 August 2018
Prerequisites: Lineer Cebir ve Diferansiyel Denklem konularında temel bilgilere sahip olunması önerilir.
Level: Fizik ve Matematik bölümlerinde 3. ve 4. sınıf öğrencileri ile lisansüstü öğrencileri için uygundur.
Abstract: Manifoldlar, Vektörler ve Kovektörler, Tensörler, Metrik Tensörü, Dış Cebir ve Uygulamaları, Stokes Teoremi, İki Boyutlu Eğrisel Yüzeyler, Metrik ve Eğrilik, Paralel Taşıma ve Türev, Kovaryant Dış Türev, Riemann Geometrisi, Otoparalel Eğriler, Jeodezik, Jeodezik Sapma Denklemi 
Language: Türkçe

Title of the course: Linear Representations of Finite Groups
Instructor: Dr. Şermin Çam Çelik
Institution: Özyeğin Ü.
Dates: 13-19 Ağustos 2018
Prerequisites: Linear algebra, basic group theory
Level: Graduate, advanced Undergraduate
Abstract: Definitions(Representations, Subrepresentations, Irreducible Representations, Equivalent Representations), Schur’ s Lemma, Character of a Representation, Orthogonality Relations for Characters, Number of Irreducible Characters, Some Basic Examples.
Language: EN, TR

Title of the course: Amenable Groups
Instructor: Prof. Ayşe Berkman, MSc. Barış Bektaş
Institution: MSGSÜ
Dates: 20-26 August 2018
Prerequisites: A course on group theory (or abstract algebra including group theory) is necessary. A course on topology will be very useful.
Level: Graduate, advanced undergraduate
Abstract: Measures and means on groups. Some properties of amenable groups. Examples and non-examples. Relation to the Banach-Tarski Paradox. Tarski numbers of groups. 
We strongly recommend for the students who are interested in geometric group theory to take Growth of Groups, Self-Similar Groups and Groups Generated by Automata, and Amenable Groups together. Even though we will try to make the three courses independent, following all three will certainly enhance understanding of the material.
Language: TR, EN

Title of the course: Growth of Groups
Instructor: Dr. Dilber Koçak
Institution: ODTÜ
Dates: 20-26 August 2018
Prerequisites: A course on group theory (or abstract algebra including group theory) is necessary.
Level: Graduate, advanced undergraduate
Abstract:
• Growth functions and growth series of groups (Preliminaries, general notions and history)
• Growth of nilpotent groups
• Growth of solvable groups
• Groups of polynomial growth (outline of Gromov’s Theorem)
• Groups of intermediate growth (Grigorchuk groups)
• Summary, final remarks and open problems.
Language: TR, EN

Title of the course: Self-similar groups and groups generated by automata
Instructor: Asst. Prof. Mustafa Gökhan Benli
Institution: ODTÜ
Dates: 20-26 August 2018
Prerequisites: A course on group theory (or abstract algebra including group theory) is necessary.
Level: Graduate, advanced undergraduate
Abstract:
• Rooted trees and their automorphisms
• Self-similar groups
• Automata and groups generated by automata
• Examples and sources of self-similar groups
• Relations with the Burnside problem
• Contracting and branch groups
• Relations with amenability and growth
Language: TR, EN

Title of the course: Prime numbers
Instructor: Prof. David Pierce
Institution: MSGSÜ
Dates: 20-26 August 2018
Prerequisites: Some elementary number theory
Level: Graduate, advanced undergraduate
Abstract: We shall work through the Prime Number Theorem, that the probability that a given number N is prime is about 1/log(N).
Language: TR, EN
Textbook or/and course webpage: http://mat.msgsu.edu.tr/~dpierce/Courses/Sirince/ (in preparation)

Title of the course: Introduction to general topology
Instructor: Dr. Matteo Paganin
Institution: Sabancı Ü.
Dates: 20-26 August 2018
Prerequisites: Just the basics.
Level: Graduate, advanced undergraduate
Abstract: In this course we plan to give definitions, examples, and basic properties of topological spaces; closed and open subsets; neighbourhoods; metric spaces; basis for topologies; continuous, open, and closed functions, homeomorphism; closure, interior, accumulation points; limits; separation axioms; compactness and connectedness. The aim of the course will be to state and sketch the proof of the Weierstrass and Heine-Borel theorems.
Language: EN, TR

Title of the course: Automorphism groups of some structures
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 20-26 August 2018
Prerequisites: TBA
Level: Undergraduate, advanced undergraduate, graduate
Abstract: TBA
Language: TR, EN

Title of the course: Molecular dynamics, Monte Carlo dynamics
Instructor: Prof. François Dunlop
Institution: Université de Cergy Pontoise
Dates: 27 August – 2 September 2018
Prerequisites: Calculus
Level: Graduate, advanced undergraduate
Abstract: The course is about time evolution of extended systems, with emphasis on what to do and understand mathematically before going on the computer.
1. Time in dynamics and algorithms
2. Molecular dynamics: Runge Kutta and Verlet algorithms
3. Molecular dynamics: ergodicity
4. Monte Carlo dynamics as a Markov chain
5. Monte Carlo: algorithms for particle systems
6. Cellular automata
Language: EN

Title of the course: Limits, Sequences and Series
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 27 August – 2 September 2018
Prerequisites: TBA
Level: Advanced undergraduate, graduate
Abstract: TBA
Language: EN, TR

Title of the course: Field Theory
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 20 August – 9 September 2018
Prerequisites: Basic abstract algebra
Level: Advanced undergraduate, graduate.
Abstract: Fields and field extensions. Theory of finite fields. Algebraic closure. Automorphisms of fields. Galois theory. Galois completion. Algebraic closure of finite fields.
Language: TR, EN

Eğitmen: Asst. Prof. Salih Durhan
Kurum: -
Tarih: 20 Ağustos – 2 Eylül 2018
Dersin Adı: Kombinasyon hesapları ve olasılık
İçerik: Asıl amacımız olasılık kuramı olacak. Olay kümemiz sonlu ya da sonsuz, ayrık ya da sonsuz olabilecek. Ama çoğu kez olasılık problemlerinde kombinasyon hesapları da gerekir. Kombinasyon hesaplarını ihtiyacımız olduğu kadar inceleyeceğiz. Her gün bir ya da iki probleme odaklanılacak. Öğrencilerin bu derste aktif olmaları beklenmektedir.

Eğitmen: Doç. Dr. Özlem Beyarslan
Kurum: Boğaziçi Ü.
Tarih: 20 Ağustos – 2 Eylül 2018
Dersin Adı: Polinomlar
İçerik: Polinom halkası ve özellikleri, formal türev, polinomların diskriminantı.

Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Ü.
Tarih: 20 Ağustos – 2 Eylül 2018
Dersin Adı: Oyunlar Kuramı
İçerik: Oyunların matematiğine odaklanacağız. Şans oyunları, şansın olmadığı oyunlar, sonlu oyunlar, potansiyel olarak sonlu oyunlar, sonsuz oyunlar... Varsa oyunların kazanan stratejilerini, yoksa kazanma olasılığımızı artıran stratejileri bulacağız. Kombinasyon hesapları ve olasılık konularına doğal olarak eğileceğiz.

Eğitmen: MSc. Kübra Dölaslan
Kurum: ODTÜ
Tarih: 20 Ağustos – 2 Eylül 2018
Dersin Adı: Problem Saati
İçerik: Bu derste, gün boyunca işlenen konularla ilgili problemler çözülecek, öğrencilerin soruları yanıtlanacaktır. Not: Problemler kolay olmayacaktır ve öğrenciden aktif katılım beklenecektir.

Title of the course: Free Modules, Abel Groups and Vector Spaces
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 20 August – 2 September 2018
Prerequisites: Basic module theory
Level: Advanced undergraduate, graduate.
Abstract: Free modules. Homomorphisms from/onto free modules. Matrices and algebra of matrices. Free modules over PID's.
Language: TR, EN

Title of the course: Logic for Artificial Intelligence
Instructor: Mr. Arif Mardin
Institution: -
Dates: 27 August – 2 September 2018
Prerequisites: Apart from motivation to follow what is going on, and familiarity with the basics of logical reasoning, no particular familiarity with any subject is needed.
Level: Undergraduate
Abstract: Logic (more precisely propositional logic and predicate logic) as a method of representation of knowledge in artificial intelligence. Well-formed formulas, unification, resolution strategies for the resolution of problems. Introduction to probabilistic reasoning and decision making under uncertain knowledge.
Language: EN
Textbook: Hodges, W.: “Logic”, Penguin Books, 1977,
Nilsson, N.J.: “Principles of Artificial Intelligence”, Morgan Kaufmann, 1980,
Genesereth, M. and Nilsson, N.J.: “Logical Foundations of Artificial Intelligence”,
Russell, S. and Norvig, P.: “Artificial Intelligence: A Modern Approach”, 3rd edn., Prentice Hall, 2013.
Genesereth, M., and Nilsson, N.J.: "Logical Foundations of Artificial Intelligence", Morgan Kaufmann, 1987.

Title of the course: Topics in Complex Function Theory, a detour around interpolation theorems
Instructor: Assoc. Prof. Uğur Gül
Institution: Hacettepe Ü.
Dates: 27 August – 2 September 2018
Prerequisites: A solid background in Graduate level Real and Complex Analysis and Functional Analysis
Level: Graduate
Abstract:
I. Infinite products, Blaschke condition, Blaschke products, Inner Functions.
II. Schwarz lemma, Schwarz-Pick lemma, Poincaré metric, Pick interpolation theorem.
III. Poisson-Jensen Formula, Hardy-Nevanlinna classes, Inner-outer factorization of Hardy Functions.
IV. An application of Blaschke products: Müntz-Szasz approximation theorem.
V. Carleson interpolation theorem.
References: "Bounded Analytic Functions" by J. B. Garnett, "Functional Analysis" by P. Lax
Language: TR, EN

Title of the course: Semisimple rings
Instructor: Assoc. Prof. Müge Taşkın
Institution: Boğaziçi Ü.
Dates: 27 August – 2 September 2018
Prerequisites: Ring theory and module theory
Level: Graduate
Abstract: After defining and studying basic properties of simple and semisimple rings, we will focus on Artinian semisiple rings. We'll prove the Artin-Wedderburn theorem which provides the classification of  Artinian semisiple rings  and the modules over them.
Language: İngilizce

Title of the course: Category Theory
Instructor: Dr. Matteo Paganin
Institution: Sabancı Ü.
Dates: 27 August – 2 September 2018
Prerequisites: Some group theory, some topology, the more the better, to have examples.
Level: Graduate, advanced undergraduate
Abstract: In this course we plan to give definitions, (plenty of) examples, and basic properties of categories, morphisms, isomorphisms, monomorphisms and epimorphisms, initial, terminal, and zero objects, functors, morphisms of functors, representable functors, and adjoints. The aim of the course will be to show how most of the common contructions in Mathematics are adjoints.
Language: TR, EN

Title of the course: Complex Analysis
Instructor: Prof. Sten Kaijser
Institution: Uppsala University
Dates: 27 August – 9 September 2018
Prerequisites:
First week: Calculus, linear algebra, complex numbers.
Second week: A first course in complex analysis.
Level: University student/graduate student (depending on audience)
Abstract:
First week: Complex numbers, analytic functions up to Cauchy formula
Second week: Some important theorems of complex analysis
Language: EN

Eğitmen: Doç. Dr. Özlem Beyarslan
Kurum: Boğaziçi Ü.
Tarih: 3-9 Eylül 2018
Dersin Adı: Sayılar Kuramı
İçerik:
Bölünebilme, Öklid algoritması
Asallar
Aritmetiğin Esas Teoremi
En büyük ortak bölen
Bezoult özdeşliği
Fermat ve Wilson Teoremleri
Euler fonksiyonu ve Euler teoremi
En küçük ortak kat
Modüler aritmetik
Bölenlerin sayısı
Bölenlerin toplamı
Mükemmel sayılar

Title of the course: Hilbert’s Axioms
Instructor: Assoc. Prof. Emre Coşkun
Institution: ODTÜ
Dates: 3-9 September 2018
Prerequisites: Familiarity with Euclidean geometry.
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: A quick overview of the first few books of Euclid’s Elements. Hilbert’s Axioms.
Language: EN, TR
Textbook or/and course webpage: Robin Hartshorne, Euclid and Beyond (ch. 2)

Title of the course: Statistical Mechanical Models on the Lattice
Instructor: Mr. Arif Mardin
Institution: -
Dates: 3-9 September 2018
Prerequisites: Some familiarity with random walk models on the lattice in d-dimensional space and discrete probabilistic models would be helpful. Basic notions of equilibrium statistical mechanics at the undergraduate level should also be useful.
Level: Advanced undergraduate, graduate
Abstract: The aim of this course is to offer a mathematically rigorous introduction to the Ising, percolation and self-avoiding walk models on the lattice in d-dimensional space. The course will focus on some of the important results obtained until now and the methods used to achieve them.
Language: EN
Textbook: Friedli, S. and Velenik, Y.: “Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction”, Cambridge University Press, 2017,
G. Grimmett: “Percolation”, 2nd edn., Springer Verlag, 1999,
Madras, N. and Slade, G.: “The Self-Avoiding Walk”, Birkhäuser, 1993.
Madras, N., and Slade, G.,: "The Self-Avoiding Walk", Birkhäuser, 1993.

Title of the course: Transform Methods for Differential Equations – A unified approach
Instructor: Dr. Konstantinos Kalimeris
Institution: University of Cambridge
Dates: 3-9 September 2018
Prerequisites: Basic knowledge of Complex Variables (An introduction to basic Complex Analysis themes will be given in the first lectures).
Level: Advanced undergraduate
Abstract: In this course we will study a class of differential equations which appear in a plethora of physical phenomena and include the heat, the wave, the Laplace, and the Helmholtz equations. Such equations for simple geometries and simple boundary conditions are traditionally solved via separation of variables or transform methods. However, these methods are limited, and even in the particular cases that they are applicable, they have several disadvantages.
After reviewing in a coherent way some of the classical transform methods, we will present a new approach, which has been acclaimed as the first major breakthrough in the solution of linear PDEs, since the discovery of the Fourier transform in the 18th century. In this course, this Unified Transform Method will be presented, making usage of basic mathematical tools and methods of complex analysis. The students will be given an overview of the several analytical and numerical advantages that this unified approach possesses. At the last lectures of the course the students will have the opportunity to apply this knowledge in a series of problems related to differential equations.
The course will also include an introduction of complex variables.
Language: EN

Title of the course: Real Analytic Functions
Instructor: Dr. Derya Çıray
Institution: Universitat Konstanz
Dates: 3-9 September 2018
Prerequisites: Basic analysis
Level: Graduate, advanced undergraduate, beginning Undergraduate
Abstract:
The aimed lecture will basically consists of the following parts:
 1. Elementary properties of Real Analytic functions (Power series,analytic continuation and more)
2. Implicit function theorem
3.The Weierstrass Preparation Theorem
Language: EN

Title of the course: Paradoxical decompositions: The Banach-Tarski paradox and others
Instructor: Asst. Prof. Burak Kaya
Institution: ODTÜ
Dates: 3-9 September 2018
Prerequisites: Basic group theory knowledge is sufficient. Some familiarity with group actions is suggested. The rest of the course will be self-contained.
Level: Advanced undergraduate, beginning Undergraduate
Abstract: We shall cover the Banach-Tarski paradox and some other paradoxical decompositions. If time permits, we may learn about amenable groups and prove some basic facts.
Textbook or/and course webpage: Stan Wagon, The Banach-Tarski Paradox, Cambridge University Press. The instructor will also provide some lecture notes.
Language: TR, EN

Title of the course: Henstock-Kurzweil integral
Instructor: Asst. Prof. Serge Randriambololona
Institution: Galatasaray Ü.
Dates: 3-9 September 2018
Prerequisites: A good understanding of a first course of analysis in one variable
Level: Graduate, advanced undergraduate, beginning Undergraduate
Abstract: The Henstock-Kurzweil integral is an integral which is more general than Riemann integral (in the sense that some non Riemann integrable functions may happen to be Henstock-Kurzweil integrable), but does not require measure theory for its definition (as opposed to Lebesgue integral).
We will quickly review the theory of Riemann integral and point-out some of its limitations. We will then discuss how the Henstock-Kurzweil integral allows one to deal with some of these limitations. If time permits, we will discuss some relations to the Lebesgue integral.
Textbook or/and course webpage:
https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/kurzweil.pdf (part of it)
Language: EN

Title of the course: Introduction to Polyhedral Geometry
Instructor: Asst. Prof. Zafeirakis Zafeirakopoulos
Institution: GTÜ
Dates: 3-9 September 2018
Prerequisites: Knowledge of basic linear algebra and basic calculus.
Level: Graduate, advanced undergraduate
Abstract:
1. Definition of Polyhedra and friends
2. H-rep, V-rep , faces and complexity
3. Combinatorics of Polytopes
4. Generating Function of cones
5. Generating Function of polyhedra
6. Applications
Language: EN

Title of the course: Yakınsama Türleri ve İlişkileri
Instructor: Prof. Şafak Alpay
Institution: ODTÜ
Dates: 3-9 September 2018
Prerequisites: -
Level: Lisans 3 ve üstü
Abstract: Fonksiyonların noktasal, düzgün ve hemen her yerde yakınsaması, L_p(l <= p < \infty) uzayında yakınsama, ölçümde yakınsama, Egoroff Teoremi, Vitali Yakınsama Teoremi, Ascoli-Arzela Teoremi, L_p uzayının Banach uzayı özellikleri.
Language: TR, EN

Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Ü.
Tarih: 3-16 Eylül 2018
Dersin Adı: Oyun ve Olasılık
İçerik: Oyunların matematiğine odaklanacağız. Şans oyunları, şansın olmadığı oyunlar, sonlu oyunlar, potansiyel olarak sonlu oyunlar, sonsuz oyunlar... Varsa oyunların kazanan stratejilerini, yoksa kazanma olasılığımızı artıran stratejileri bulacağız. Kombinasyon hesapları ve olasılık konularına doğal olarak eğileceğiz.

Eğitmen: Prof. Melih Boral
Kurum: -
Tarih: 3-16 Eylül 2018
Dersin Adı: Polinomlar ve Cebirsel Sayılar
İçerik: Polinomlar ve polinom fonksiyonları, bölme algoritması, polinomların rasyonel kökleri, cebirsel sayılar ve polinomları, indirgenemez polinomlar.

Eğitmen: MSc. Kübra Dölaslan
Kurum: ODTÜ
Tarih: 3-16 Eylül 2018
Dersin Adı: Problem Saati
İçerik: Bu derste, gün boyunca işlenen konularla ilgili problemler çözülecek, öğrencilerin soruları yanıtlanacaktır. Not: Problemler kolay olmayacaktır ve öğrenciden aktif katılım beklenecektir.

Eğitmen: Prof. Haluk Oral
Kurum: -
Tarih: 10-16 Eylül 2018
Dersin Adı: Matematik Sohbetleri
İçerik: Sayma problemleri, reel sayıların bazı özellikleri, Binom teoremi, Öklid algoritması, şifreleme.

Title of the course: Classical Construction Problems in Geometry
Instructor: Assoc. Prof. Emre Coşkun
Institution: ODTÜ
Dates: 10-16 September 2018
Prerequisites: Familiarity with Euclidean geometry is a must, experience with fields and field extensions is a plus.
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: The three classical problems in geometry: quadrature of the circle, trisection of the angle, duplication of the cube. Fields and field extensions. Constructible numbers. Impossibility of the solutions of the three classical problems with ruler and compass.
Language: EN, TR
Textbook or/and course webpage: Robin Hartshorne, Euclid and Beyond (ch. 6)

Title of the course: Construction of the real numbers
Instructor: Dr. Denis Chéniot
Institution: Université de Marseille
Dates: 10-16 September 2018
Prerequisites: First year of university
Level: Advanced undergraduate   
Abstract: Construction of the real numbers by cuts. Theorem of the least upper bound, convergence of bounded monotone sequences, convergence of Cauchy sequences. Construction of the real numbers by Cauchy sequences, equivalence of the two constructions. Characterization of the order type of the set of real numbers as having a countable dense subset, no maximum or minimum and no gaps.
Language: EN, TR

Title of the course: Axiom of determinacy and some of its consequences
Instructor: Asst. Prof. Burak Kaya
Institution: ODTÜ
Dates: 10-16 Eylül 2018
Prerequisites: Exposure to topology of metric spaces is required. Little exposure to Lebesgue measure is suggested but not required, as we shall go over the construction. It may help to be acquainted with the axiom of choice and its variants, though, knowledge on axiomatic set theory is not required.
Level: Graduate, advanced undergraduate
Abstract: We shall first introduce infinite games on natural numbers and the axiom of determinacy (AD) which states that all such games have winning strategies for one of the two players. We will then cover some consequences of AD, without assuming the axiom of choice. Finally, we will cover some determinacy results such as the Gale-Stewart theorem, assuming the axiom of choice.
Textbook or/and course webpage: Relevant parts of the book “Set Theory, The Third Millenium Edition” by Thomas Jech. The instructor will also provide some lecture notes.
Language: TR, EN

Title of the course: Introcduction to Convex Optimization
Instructor: MSc. Oğuzhan Yürük
Institution: Technische Universität Berlin
Dates: 10-16 September 2018
Prerequisites: Basic Linear Algebra
Level: Advanced undergraduate, beginning Undergraduate
Abstract: This  will be an introductory course on convex optimization. Participants are expected  to have a basic knowledge of linear  algebra.   A background on optimization is not  required  however it can be useful.  The  main  goal of this  course is to provide  participants with  the  required  understanding of convex optimization in order  to study  conic programming.  During  the  6 days  we will cover the following:
• Day  1: The notation that will be used throughout the course will be set.  Preliminary results coming from the linear algebra  will be given
• Day  2: The notions  of affine hull, convex hull and conic hull will be introducted and we will see the Carathedory’s theorem  on convex hulls.
• Day  3: We will cover the operations that preserve convexity.  Then we will prove an important result  of convexity,  seperating hyperplane theorem.
• Day  4: Definition of a convex function  and operations that preserve convex functions  will be given.  The first and second order convexity  conditions  for functions  will be shown and used to verify some important examples of convex functions.
• Day  5: The notion of convex optimization problem will be introduced with the notation that comes with it.  First  order optimality conditions  will be proven.
• Day  6: We will focus on generalized  cone inequalities  and  then  understand what  is a conic programming problem  why it is a convex problem.
Language: EN

Title of the course: Banach Uzayları ve Üzerlerindeki Sınırlı Doğrusal Dönüşümler
Instructor: Prof. Şafak Alpay
Institution: ODTÜ
Dates: 10-16 September 2018
Prerequisites: -
Level: Lisans 4 ve üstü
Abstract: Sonlu boyutlu normlu uzaylar, Banach-Steinhaus Teoremi, Açık Gönderim Teoremi, Hahn-Banach Teoremi, L_p uzaylarının Banach uzayı özellikleri.
Language: EN, TR

Title of the course: Percolation on Lattices
Instructor: MSc. Pal Galicza
Institution: Renyi Institute, Budapest
Dates: 10-16 September 2018
Prerequisites: A course in probability theory and basic knowledge of calculus and graph theory is necessary.
Level: Advanced undergraduate, graduate
Abstract: Percolation is perhaps the simplest model of statistical physics exhibiting phase transition. The main focus of the course will be on plane lattices, but if there is interest we shall investigate different graphs and groups. We will prove that the critical probability on the square lattice is 1/2 and that at criticality there is no percolation. Finally, we shall sketch the proof of Smirnov's celebrated theorem on the conformal invariance of the limit of percolation probabilities.
Language: EN
Textbook: Bollobas -Riordan: Percolation, Grimmett: Percolation

Title of the course: Ölçüm Teorisi ve İntegral
Instructor: Prof. Zafer Ercan
Institution: AİBÜ
Dates: 10-16 September 2018
Prerequisites: -
Level: Lisans 3 ve üstü
Abstract: Sigma cebirlerinde ölçüm kavramı, ölçülebilir kümeler ve fonksiyonlar, Lebesgue ölçüm, çeşitli yakınsaklık kavramları ve İntegrallenebilir fonksiyonlar.
Language: EN, TR

Title of the course: "Learning-Teaching-Researching Mathematics"
Instructor: Prof. Alexandre Borovik
Institution: Manchester U.
Dates: 3 - 16 September 2018
Prerequisites: Interest to mathematics
Level: All levels, from schoolchildren to teachers
Abstract: The course is based on my books and papers about mathematical thinking and mathematical practice.
Language: English

Title of the course: Singular curves (Tekil eğriler)
Instructor: Prof. Ferit Öztürk
Institution: Boğaziçi Ü.
Dates: 10-16 September 2018
Prerequisites: Analysis, algebra
Level: higher undergrad, grad
Abstract: Analytic curves in C^2 are 2-manifolds. In this course, we investigate the topology of those curves with an isolated singularity at the origin. We will talk about the Newton polygon, the Puiseux series and a bit of knots. The course will be self-contained. (C^2'de karmaşık analitik eğriler, iki boyutlu manifoldlardır. Orijinde tek bir tekilliği olan eğrilerin topolojisi hakkında konuşacağız. Newton poligonu, Puiseuex serileri ve bir miktar düğümler içeren bu ders, ihtiyacı olan her topolojik/geometrik kavramı kendi kuracak.)
Language: TR or ENG, depending on the audience

Title of the course: Introduction to probability theory
Instructor: Prof. Eduard Emelyanov
Institution: ODTÜ
Dates: 10-16 September 2018
Prerequisites: Basic calculus and linear algebra
Level: Undergraduate
Abstract: Random vectors and sequences.
Law of large numbers. Markov chains with finite number of states. Problems solving.
Language: EN

Title of the course: Transfinite induction and well-ordered sets.
Instructor: Dr. Denis Chéniot
Institution: Université de Marseille
Dates: 17-23 September 2018
Prerequisites: First year of university
Level: Advanced undergraduate   
Abstract: Examples of the use of transfinite induction in mathematics. Definition and elementary properties of the well-ordered sets. Proof and definition by transfinite induction, with an emphasis on the justification of the latter. Comparability of well-ordered sets. Proof of the well-orderability of every set (Zermelo's theorem).        
Language: EN

Title of the course: Solvable and Nilpotent Groups
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 17-23 September 2018
Prerequisites: A good course in Group Theory.
Level: Advanced undergraduate, graduate.
Abstract: Commutators, commutator calculus. Derived subgroups. Central series. Solvable and nilpotent groups. Examples of linear groups: Borel subgroup and unipotent subgroups.
Language: TR, EN

Title of the course: Quadratic Forms
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 17-23 September 2018
Prerequisites: Linear Algebra.
Level: Advanced undergraduate, graduate.
Abstract: We will classify quadratic forms over real numbers, complex numbers and finite fields.
Language: TR, EN

Title of the course: Invariants of Permutation Groups
Instructor: MSc. Hülya Duyan
Institution: Central European University
Dates: 17-23 September 2018
Prerequisities: Basic group theory and graph theory
Level: Undergraduate, graduate
Abstract: The base size of a group and the metric dimension of a graph were introduced around 40 years ago. They are used in different areas such as computational group theory and the graph isomorphism problem. Since the introduction of distinguishing number of permutation groups, many connections between base size, metric dimension and distinguishing number have been discovered. In this course, we shall study these concepts, their relations and cover some applications.
Language: TR,EN