Toplu Ders İçerikleri

Title of the course: Bilim ve bilimsel gelişmeler
Instructor: Dr. Vedat Tanrıverdi
Institution: -
Dates: 15-21 July 2019
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: Lie ve Leibniz cebirlerine giriş
Instructor: Dr. Nil Mansuroğlu
Institution: Ahi Evran Üniversitesi
Dates: 15-22 July 2018
Prerequisites: -
Level: Graduate, advanced undergraduate
Abstract:
15.07.19 Lie cebir, Lie alt cebir tanımı ve örnekleri
16.07.19 Lie cebirlerinde ideal tanımı ve özellikleri
17.07.19 Nilpotent Lie cebirleri, Çözülebilir Lie cebirleri
18.07.19 –
19.07.19 Leibniz cebir, Leibniz alt cebir tanımı ve örnekleri
20.07.19 Leibniz cebirlerinde ideal tanımı ve özellikleri, Lie cebirleri ile Leibniz cebirleri arasındaki farklar ve benzerlikler
21.07.19 Nilpotent Leibniz cebirleri, Çözülebilir Leibniz cebrleri
Language: TR

Title of the course: Ağaçlar
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 15-21 July 2019
Prerequisites: -
Level: Beginning undergraduate, undergraduate
Abstract: Bazı kavramlar matematiğin hemen her dalında karşımıza çıkarlar. "Ağaç" kavramı bunlardan biridir. Örneğin, her aşamada iki karardan birini verdiğiniz bir oyun düşünün, bu aslında bir ağaçtır. Ya da bir yol düşünün, her 100 metrede bir üçe ayrılıyor, ya da bazen ikiye bazen üçe ayrılıyor, ama hiç geriye dönmüyor. Bu da bir ağaçtır. Bu derste, ağaçlarla matematiğin çeşitli konuları arasındaki bağı göreceğiz. Reel sayılar, tam sayılar, oyunlar, p-sel sayılar, olasılık, polinomlar içinde ağaç göreceğimiz konulardan bazıları olacak.
Language: TR, EN

Eğitmen: Doç. Dr. Özlem Beyarslan
Kurum: Boğaziçi Ü.
Tarih: 15-21 Temmuz 2019
Dersin Adı: Sayılar Kuramı
İçerik: Doğal Sayılar, tamsayılar, tümevarım, bölünebilme, en büyük ortak bölen, öklid algoritması, asallar, aritmetiğin temel teoremi, modüler aritmetik, aritmetik fonksiyonlar ve özellikleri.

Title of the course: Introduction to Group Theory, Examples, Problem Hours
Instructor: MSc. Kübra Dölaslan
Institution: ODTÜ
Dates: 15-28 July 2019
Prerequisites: The student should attend the course with the same name given by Ali Nesin.
Level: Beginning undergraduate, undergraduate
Abstract: We will discuss some examples and problems about the concepts taught in the main lecture by Ali Nesin.
Language: TR, EN

Title of the course: Introduction to Axiomatic Set Theory
Instructor: Prof. Alexei Muravitsky
Institution: Northwestern State University
Dates: 15-28 July 2019
Prerequisites: There are no special technical prerequisites; however, familiarity with the grammar and terminology of set-theoretic language and that of formal logic would be a great help.
Level: Graduate, advanced undergraduate
Abstract: The course adopts an intuitive stance to the subject (set theory) before launching into formal axiomatic development. This policy is supposed to engender an easy feel for set-theoretic concepts. Prerequisites: There are no special technical prerequisites; however, familiarity with the grammar and terminology of set-theoretic language and that of formal logic would be a great help. E-copies of the books that are listed below will be provided.
Language: EN
Textbooks: (Main text) K. Hrbacek and T. Jech, Introduction to Set Theory, third edition, revisited, and expanded, Marcel Dekker, 1999.
(supplementary texts)
• R. L. Vaught, Set Theory, An Introduction, second edition, Birkhäuser, 1995.
• J. Barwise (editor), Handbook of Mathematical Logic, Elsevier, 1993.
• I. Lavrov and L. Maksimova, Problems in Set Theory, Mathematical Logic and the Theory of Algorithms, Kluwer Academic/Plenum Publishers, 2003.
• A. Levy, Basic Set Theory, Springer-Verlag, 1979.
• J. Malitz, Introduction to Mathematical Logic: Set Theory, Computable Functions, Model Theory, Springer-Verlag New York, Inc., 1979.
• P. Halmos, Naïve Set Theory, Springer-Verlag, 1974.
• M. Hallett, Cantorian Set Theory and Limitation of Size, Clarendon Press, 1984.

Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Ü.
Tarih: 15-28 Temmuz 2019
Dersin Adı: Grup örnekleri ve temel grup teori
İçerik: Grup teori oldukça zor bir konudur, kolay kolay özümsenmez genellikle. Bu derste onlarca grup örneği vererek grup teorisini öğrenci için daha kolay anlaşılır bir hâle getirmeye çalışacağım. Başlangıçta hemen hiç teori yapmayacağız. Zaman ilerledikçe teorinin dozunu artıracağım. Yoğunlaşma gerektiren bir ders olacak.

Eğitmen: Prof. Yusuf Ünlü
Kurum: Yeditepe Ü.
Tarih: 15-28 Temmuz 2019
Dersin Adı: Halka Örnekleri
İçerik: Tam sayılar halkası. Z’de Bölme algoritması. Z[i] Gauss halkası. Z[i] de bölme algoritması. Polinomlar. Q rasyonel sayılar halkası. Q[X] polinom halkası.
Q[X] de bölme algoritması. Öklidyen bölgeler. Tek türlü çarpanlara ayrılabilme. Gauss önsavı. Z[X] de tek türlü çarpanlara ayrılabilme.

Eğitmen: MSc. Kübra Dölaslan
Kurum: ODTÜ
Tarih: 15-28 Temmuz 2019
Dersin Adı: Problem Saati
İçerik: Lise programındaki derslerde öğretilen kavramlar üzerine problemler sorup birlikte tartışacağız.


Title of the course: Temel türevli (differential) denklemlerin fizikte kullanımı
Instructor: Dr. Vedat Tanrıverdi
Institution: -
Dates: 22-28 July 2019
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: Elektrik
Instructor: Dr. Vedat Tanrıverdi
Institution: -
Dates: 22-28 July 2019
Prerequisites: -
Level: Beginning undergraduate
Abstract: Coulumb yasası ile başlayıp Maxwell denklemlerinden elektirkle ilgili olanların differansiyel haline kadar işlenecektir
Language: TR

Title of the course: Numbers and Polynomials
Instructor: Prof. Alexandre Borovik
Institution: University of Manchester
Dates: 22-28 July 2019
Prerequisites: Reasonable mastery of secondary school algebra. Suitable for fresh entrants to university or even high school students (if they understand English).
Level: Beginning Undergraduate, highschool
Abstract: The course deals with basic number theory (that is, integers) and polynomials, as concrete, sensible, sound, familiar to students objects, but treats them with full proofs in an unifying approach.
1. Taking possibility of division (of integers and polynomials over a field) with remainder for granted, a sequence of results about greatest common divisors, uniqueness of factorisation, etc. -- up to the Chinese Reminder Theorem and Lagrange's Interpolation Formula, will be *proved*. More precisely, every theorem will be formulated in two versions: for integers and for polynomials, with only one of them being proved in a lecture, the other one left as an exercise for students.
2. This part of the course will be rounded up by an explanation that the Chinese Reminder Theorem and Lagrange's Interpolation Formula are *one and the same thing*.
3. Then complex numbers and roots of unity will be introduced, and the Fundamental Theorem of Algebra stated, unfortunately, without proof.
4. And, finally a version of the Fermat's Theorem will be proved:
The equation X^n + Y^n = Z^n, n >1, has no solutions in polynomials X = X(t), Y = Y(t), Z = Z(t) of non-zero degree, with some historical remarks.
Language: EN

Title of the course: Complex Analysis
Instructor: MSc. Andrea Tomatis
Institution: Beuth Hochschule fuer Technik Berlin
Dates: 22-28 July 2019
Prerequisites: Analysis in R^n, Linear Algebra
Level: Advanced undergraduate  
Abstract: This is a basic course in complex analysis. We will treat holomorphic functions, the Cauchy-Riemann equations, conformal mappings, the Cauchy theorem, the residue theorem, Laurent series, the monodromy theorem, Picard’s theorem.
Language: EN
Textbook:
Complex Analysis, Eberhard Freitag and Rolf Busam, Springer Verlag 2009,
Complex Analysis 3rd Edition, Lars Ahlfors, McGraw Hill 1979

Title of the course: Analizde Bazı Problemler
Instructor: Prof. Mehmet Cenkci
Institution: Akdeniz Ü.
Dates: 22-28 July 2019
Prerequisites: Temel analiz dersleri.
Level: Lisans, lise (ileri).
Abstract: Fonksiyonlar, diziler ve limitler, eşitsizlikler, türev ve integral konularından ilginç problemler çözülecektir.
Language: TR
Textbook or/and course webpage:
1. H.İ. Karakaş, İ. Aliyev, Analiz ve Cebirde İlginç Olimpiyat Problemleri ve Çözümleri, Palme, 2012.
2. W.J. Kaczor, M.T. Nowak, Problems in Mathematical Analysis, Volumes I, II, and III, AMS, 2000, 2001, 2003.
3. B. Gelbaum, Problems in Analysis, Springer, 1982.
4. P.N. de Souza, J.-N. Silva, Berkeley Problems in Mathematics, Springer, 2004.

Title of the course: Analitik sayılar teorisinden seçme konular
Instructor: Dr. Cihan Pehlivan
Institution: -
Dates: 22-28 July 2019
Prerequisites: -
Level: Undergraduate, graduate
Abstract: Basic Notations, Some elementary Sieves, The normal order method, The Turan Sieve, The sieve of eratosthenes.
Language: EN, TR

Title of the course: Zeta Functions and the Heisenberg Group
Instructor: Dr. E. Mehmet Kıral
Institution: Sophia University
Dates: 22-28 July 2019
Prerequisites: Enough mathematical maturity to not be dismayed by seeing a Fourier transform, or hearing the phrase representation theory. We can define any desired term, but you should be comfortable with not necessarily knowing the whole theory that is behind them with full rigour.
Although no particular knowledge is absolutely necessary, it is a reasonable assumption that if ALL  of the following phrases are completely new to you, then you would have a difficult time trying to follow the lectures (some new words is ok): Square integrable functions, Hilbert Space, Unitary Operator,  Unitary Representation of a group, Riemann Zeta function, Functional Equation, Gamma function, holomorphic function (analytic continuation), Matrix Group,  Diagonalization.
Level: Graduate, advanced undergraduate
Abstract: I would like to emphasize the role of harmonic analysis in the functional equations of the Riemann zeta function, the Hurwitz zeta functions and other L-functions. The Fourier transform and its relation to the functional equation is encoded in the representation theory of the Heisenberg group.
Further topics at the intersection of number theory and harmonic analysis can be discussed.
Language: TR, EN

Title of the course: Quaternions
Instructor: Prof. Adrien Deloro
Institution: Sorbonne Université
Dates: 22 July – 4 August 2019
Prerequisites: Real and complex numbers. Linear algebra. Some group theory
Level: Graduate, advanced undergraduate
Abstract: Quaternions were discovered in the XIXth century by Hamilton. They generalise complex numbers in a very interesting manner. The course will describe them, and see them in relation with linear algebra (matrix theory) and geometry (isometries of R^3).
Language: EN

Title of the course: Lie algebras
Instructor: Assoc. Prof. Şükrü Yalçınkaya
Institution: İstanbul Ü.
Dates: 22 July – 4 August 2019
Prerequisites: Good knowledge of linear algebra, basics of group theory.
Level: Graduate, advanced undergraduate
Abstract: In the first week, we study some of the fundamental facts about Lie algebras over the complex field. We start by various important examples of Lie algebras and continue with discussing exponential map,  solvable and nilpotent Lie algebras and Cartan decomposition. In the second week, we study the root systems and the structure of their Weyl groups.
Language: TR, EN

Title of the course: Black box fields
Instructor: Prof. Alexandre Borovik
Institution: University of Manchester
Dates: 29 July – 4 August 2019
Prerequisites: Linear algebra, basic abstract algebra
Level: Graduate and advanced undergraduate
Abstract:
* Algebraic cryptography: finite fields, the Diffie-Hellman key exchange, some other basic protocols.
* One-way functions, the Discrete Logarithm Problem.
* Homomorphic encryption.
* Basic concepts of black box algebra. Black box groups, rings, fields.
* Structural analysis of black box fields of characteristic 2.
Language: EN

Title of the course: Complex Analysis
Instructor: MSc. Andrea Tomatis
Institution: Beuth Hochschule fuer Technik Berlin
Dates: 22-28 July 2019
Prerequisites: Analysis in R^n, Linear Algebra
Level: Advanced undergraduate  
Abstract: This is a basic course in complex analysis. We will treat holomorphic functions, the Cauchy-Riemann equations, conformal mappings, the Cauchy theorem, the residue theorem, Laurent series, the monodromy theorem, Picard’s theorem.
Language: EN
Textbook:
Complex Analysis, Eberhard Freitag and Rolf Busam, Springer Verlag 2009,
Complex Analysis 3rd Edition, Lars Ahlfors, McGraw Hill 1979

Title of the course: Analytic Tools in Number Theory
Instructor: Prof. Mehmet Cenkci
Institution: Akdeniz Ü.
Dates: 29 July – 3 August 2019
Prerequisites: Necessary background will be summarized during the course.
Level: Graduate, advanced undergraduate
Abstract: We will discuss topics in Chapter 9 of Cohen’s book, Number Theory Volume II: Analytic and Modern Tools. More specifically, Bernoulli numbers and polynomials, real and complex gamma functions, integral transforms and Bessel functions will be the topics to be covered.
Language: TR, EN
Textbook or/and course webpage:
1. H. Cohen, Number Theory, Volume II: Analytic and Modern Tools, Springer, 2007.

Title of the course: Group Actions and Sylow Theorems
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 29 July – 4 August 2019
Prerequisites: Temel grup teorisi
Level: Graduate, advanced undergraduate
Abstract: As in the title.
Language: TR, EN

Title of the course: Group Actions and Sylow Theorems, Problem Hours
Instructor: MSc. Kübra Dölaslan
Institution: ODTÜ
Dates:29 July – 4 August 2019
Prerequisites: The student should attend the course with the same name given by Ali Nesin.
Level: Graduate, advanced undergraduate
Abstract: We will discuss some examples and problems about the concepts taught in the main lecture by Ali Nesin.
Language: TR, EN

Title of the course: Elementer Sayılar Teorisi
Instructor: Dr. Cihan Pehlivan
Institution: -
Dates: 29 July – 4 August 2019
Prerequisites: -
Level: Lisans 1, 2
Abstract: Özel aritmetik dizilerde asalların sonsuzluğu, Fermat Sayıları, Mersenne sayıları, Fermat'ın küçük teoremi ve genelleştirilmesi, çarpanlara ayırma algoritmaları... (Dersimiz öğrencilerle aktif bir şekilde işlenecek olup, isteyen öğrenciler bazı derslerde kısa sunumlar yapacaktır).
Language: TR, EN

Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Ü.
Tarih: 29 Temmuz – 11 Ağustos 2019
Dersin Adı: Kombinasyon Hesapları
İçerik: Kombinasyon hesapları oldukça geniş bir konudur. Bu derste her liselinin bilmesi gerekenleri kanıtlarıyla beraber gösterdikten ve birçok örnek verdikten sonra, üreteç fonksiyonlarından hareketle çok daha derin sonuçlara varacağız.

Eğitmen: Dr. Tülay Ayyıldız Akoğlu
Kurum: Karadeniz Teknik Üniversitesi
Tarih: 29 Temmuz- 11 Ağustos
Dersin Adı: Bilgisayar Cebiri
İçerik: Matematikteki önemli bazı problemleri çözmek için temel teori ve algoritmalar. Tamsayılar, asallık testleri, tamsayıları çarpanlarına ayırmak, Öklid algoritmasi, resultantlar, Gröbner tabanları, polinom sistemlerinin çözümleri. Sembolik ve nümerik (Hibrit) hesaplama.

Eğitmen: Dr. Kemal Akoğlu
Kurum: NC State University
Tarih: 29 Temmuz – 11 Ağustos 2019
Dersin Adı: Olasılık ve Veri Bilimine Giriş
İçerik: Sayma; permutasyon ve kombinasyon; belirsizlik ve rasgelelik kavramları; rasgele değişkenler ve olaylar; bağımsızlık kavramı ve koşullu olasılık; olasılıkta kavramsal yanılgılar; istatistik ve veri bilimine ilişkin temel kavramlar; istatistiksel araştırma döngüsü; istatiksel çıkarım ve modellemenin temelleri.

Eğitmen: Doç. Dr. Özlem Beyarslan
Kurum: Boğaziçi Ü.
Tarih: 29 Temmuz – 11 Ağustos 2019
Dersin Adı: Çizge Kuramı
İçerik: Çizgeler teorisinin temel tanımları, güvercin yuvası prensibi, sayma kuralları, çizgelerde tümevarım, düzlemsel çizgeler, çizgeleri boyama, Ramsey sayıları, sonsuz Ramsey teoremi, Hall evlilik teoremi, ağaçlar.

Title of the course: Black Box rings
Instructor: Prof. Alexandre Borovik
Institution: University of Manchester
Dates: 5-11 August 2019
Prerequisites: Linear algebra, basic abstract algebra
Level: Graduate and advanced  undergraduate
Abstract:
* Homomorphic encryption
* Basic concepts of black box algebra. Black box groups, rings, fields.
* Structural analysis of black box matrix rings over finite fields.
Language: EN

Title of the course: Probability with problems
Instructor: Dr. Kerem Altun
Institution: Işık Ü.
Dates: 5-11 August 2019
Prerequisites: High school level probability theory
Level: Beginning undergraduate
Abstract: We will discuss probability theory through problems available in the Android app titled “Probability Puzzles”. The app covers fundamental concepts in probability theory, starting from basic level dice-rolling problems to advanced level problems involving Markov chains and martingales. We will try to cover all problems in the app, pushing the students in class to their limits.
Language: TR, EN

Title of the course: Introduction to Ring Theory
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 5-11 August 2019
Prerequisites: -
Level: Beginning undergraduate, undergraduate
Abstract: As in the title.
Language: TR, EN

Title of the course: Introduction to Ring Theory, Problem Hours
Instructor: MSc. Kübra Dölaslan
Institution: ODTÜ
Dates: 5-11 August 2019
Prerequisites: The student should attend the course with the same name given by Ali Nesin.
Level: Graduate, advanced undergraduate
Abstract: We will discuss some examples and problems about the concepts taught in the main lecture by Ali Nesin.
Language: TR, EN

Title of the course: Field Theory
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 5-11 August 2019
Prerequisites: Linear Algebra
Level: Graduate, advanced undergraduate
Abstract: Field extensions, splitting fields and normal extensions, algebraic closure, inseperable extensions, finite fields.
Language: TR, EN

Title of the course: Nonlinear Dynamics and Chaos
Instructor: Dr. Deniz Eroğlu
Institution: Kadir Has Ü.
Dates: 5-11 August 2019
Prerequisites: Single-variable calculus, curve sketching, Taylor series, separable differential equations, linear algebra.
Level: Graduate, advanced undergraduate
Abstract: Dynamical system theory is interested in the evolution of systems. It tries to understand the processes in motion and limitation (stability) of systems. Chaos in dynamics is one of the scientific revolutions of the twentieth century, that deepened our understanding of the nature of unpredictability. In this course, we will discuss the fundamentals of these theories.
Language: TR; EN

Title of the course: PIDs and UFDs
Instructor:
Prof. Ali Nesin
Institution:
İstanbul Bilgi Ü.
Dates:
12-18 August 2019
Prerequisites:
Basic algebra
Level:
Graduate, advanced undergraduate
Abstract: We will prove basic results about PID's and UFD's. We will try to give some nontrivial examples.
Language: TR, EN

Title of the course: PIDs and UFDs, Problem Hours
Instructor: MSc. Kübra Dölaslan
Institution: ODTÜ
Dates: 12-18 August 2019
Prerequisites: The student should attend the course with the same name given by Ali Nesin.
Level: Graduate, advanced undergraduate
Abstract: We will discuss some examples and problems about the concepts taught in the main lecture by Ali Nesin.
Language: TR, EN

Title of the course: Galois Theory
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 12-18 August 2019
Prerequisites: Linear algebra and familiarity with algebraic structures, like groups rings fields.
Abstract: Galois extensions, examples and applications,, cyclic extensions solvable and radical extensions.
Level: Graduate, advanced undergraduate
Language: TR, EN

Eğitmen: Mr. Ali Törün
Kurum: -
Tarih: 12-25 Ağustos 2019
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: Prof. Ali Nesin
Kurum: İstanbul Bilgi Ü.
Tarih: 12-25 Ağustos 2019
Dersin Adı: Oyun ve Matematik
İçerik: Şans oyunları dahil, oyunların içindeki matematikten sözedeceğiz. Tabii ki olasılık işin işine girecek, ama şans oyunları dışındaki oyunları da irdeleyip kazanan strateji konusunu irdeleyeceğiz. Nash dengesi de işleyeceğimiz konulara dahil olacak, ama daha çok örneklerden yola çıkacağımız için izlemesi kolay bir ders olacağını düşünüyorum.

Eğitmen: Doç. Dr. Özlem Beyarslan
Kurum: Boğaziçi Ü.
Tarih: 12-25 Ağustos 2019
Dersin Adı: Sayılar Kuramı
İçerik: Doğal Sayılar, tamsayılar, tümevarım, bölünebilme, en büyük ortak bölen, öklid algoritması, asallar, aritmetiğin temel teoremi, modüler aritmetik, aritmetik fonksiyonlar ve özellikleri.

Eğitmen: MSc. Kübra Dölaslan
Kurum: ODTÜ
Tarih: 12-25 Ağustos 2019
Dersin Adı: Problem Saati
İçerik: Lise programındaki derslerde öğretilen kavramlar üzerine problemler sorup birlikte tartışacağız.

Title of the course: An introduction to social choice theory
Instructor: Prof. Remzi Sanver
Institution: CNRS, Universite Paris Dauphine
Dates: 19-25 August 2019
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: TR, EN

Title of the course: Introduction to Module Theory
Instructor:
Prof. Ali Nesin
Institution:
İstanbul Bilgi Ü.
Dates:
19-25 August 2019
Prerequisites:
Ring theory
Level:
Graduate, advanced undergraduate
Abstract: As in the title.
Language: TR, EN

Title of the course: Introduction to Module Theory, Problem Hours
Instructor: MSc. Kübra Dölaslan
Institution: ODTÜ
Dates: 19-25 August 2019
Prerequisites: The student should attend the course with the same name given by Ali Nesin.
Level: Graduate, advanced undergraduate
Abstract: We will discuss some examples and problems about the concepts taught in the main lecture by Ali Nesin.
Language: TR, EN

Title of the course: Valued Fields
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 19-25 August 2019
Prerequisites: field theory and galois theory
Level: Graduate, advanced undergraduate
Abstract: Valuations, places and valuation Rings, Discrete valuations. Extensions of valuations. Decomposition and inertia group, linear disjointness of fields.
Language: TR, EN

Title of the course: Operator Theory on Hilbert Spaces- an Introduction
Instructor: Dr. Elif Uyanık, Dr. Başak Koca, Assoc. Prof. Uğur Gül
Institution: Yozgat Bozok Ü., İstanbul Ü., Hacettepe Ü.
Dates: 19 August – 8 September 2019
Prerequisites: Yüksek lisans düzeyinde reel analiz bilgisi
Level: Yükseklisans
Abstract:
I. week (Elif UYANIK)
I. Functional Analysis Preliminaries: normed spaces, Banach spaces, bounded operators
II. Hahn-Banach theorem, dual maps
III. Baire Category theorem and consequences.
IV. Inner product spaces, Cauchy-Schwarz inequality, Hilbert spaces.
V. Hilbert Spaces, Orthonormal systems, basis
II. week (Başak KOCA)
I. Banach algebras, spectrum, spectral radius, unitization, Neumann series.
II. Gelfand-Mazur theorem, Spectral mapping theorem, spectral Radius formula.
III. Closed ideals, maximal ideals, maximal ideal space.
IV. Commutative Banach algebras, Gelfand transform.
V. C*-algebras, commutative C*-algebras, Gelfand-Naimark Theorem.
III. week (Uğur GÜL)
I. Operators on Hilbert spaces, Self-adjoint, unitary, normal operators, Isometries.
II. Spectral resolution of normal operators, L\infty functional calculus.
III. Topologies on B(H): weak operator topology, strong operatör topology, Von-Neumann bicommutant theorem, Von Neumann algebras
IV. projections and projection lattices in B(H)
V. Commutative Von-Neumann algebras.
References: 1. "Introduction to Functional Analysis" by R. Meise and D. Vogt, Oxford Science Publications, 1997
2. "C*-algebras and Operator Theory" by G. Murphy, Academic Press, 1990
3. "Fundamentals of the Theory of Operator Algebras" by R. Kadison and J. R. Ringrose, Academic Press, 1983.
Language: EN

Title of the course: Basic 3-Manifold Topology
Instructor: Dr. Agustin Moreno
Institution: University of Augsburg
Dates: 19 August – 1 September 2019
Prerequisites: Point set topology, basic algebraic topology
Level: Graduate, advanced undergraduate
Abstract: In this lecture, we will cover basic topics in 3-mfld topology, prime decomposition, torus decomposition, Seifert manifolds, JSJ Decomposition, Geometrization Conjecture.
Textbook or/and course webpage: Allen Hatcher-Notes on Basic 3-Manifold Topology
Language: EN

Title of the course: Classification of surfaces
Instructor: Dr. Merve Seçgin
Institution: TED Ü.
Dates: 19 August – 1 September 2019
Prerequisites: Point set topology, Basic algebraic topology
Level: Graduate, advanced undergraduate
Abstract: In this lecture, we will touch upon the classification of surfaces, triangulation of surfaces and relation with knot theory.
Textbook or/and course webpage: An Introduction to Topology The Classification theorem for Surfaces By E. C. Zeeman
Language: TR, EN

Title of the course: Topics in Number Theory
Instructor: Asst. Prof. Haydar Göral
Institution: Dokuz Eylül Ü.
Dates: 19 August – 1 September 2019
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: Several proofs of the infinitude of primes, sums over primes, distribution of prime num-bers, sieve methods
Second week: Arithmetic combinatorics, arithmetic progressions, graphs, additive number theory
Language: TR, EN

Title of the course: Arf Rings
Instructor: Prof. Ali Sinan Sertöz
Institution: Bilkent Ü.
Dates: 26 August – 1 September 2019
Prerequisites: Arf uses only elementary techniques but with an admirable degree of mathematical maturity. Therefore a must prerequisite is willingness to learn something new. For undergrads, if you know what a ring is then you are set to go. If not, I will define that too!
Level: Graduate, advanced undergraduate
Abstract: The aim of the course is to explain the original definition and the use of Arf rings as Arf himself did. We will start by defining the basics of curve singularities, their resolutions and the multiplicities involved. The motivating problem is to find these multiplicities that occur during the resolution process. I will explain Du Val’s geometric solution. At this point Du Val poses the challenge of finding these multiplicities once the local parametrization of the singularity is given. Arf solves this algebraic problem by defining some special rings which he called canonical rings and which are today known as Arf rings. I will go step by step through Arf’s original article and explain his solution and calculations. At the end, if time permits I may talk about Lipman’s generalization of Arf rings in the language of commutative algebra.
Language: EN, TR

Title of the course: Free Modules
Instructor:
Prof. Ali Nesin
Institution:
İstanbul Bilgi Ü.
Dates:
26 August – 1 September 2019
Prerequisites:
Ring theory
Level: Graduate, advanced undergraduate
Abstract: As in the title
Language: TR, EN

Title of the course: Profinite Groups
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 26 August – 1 September 2019
Prerequisites: group theory, field theory
Level: Graduate, advanced undergraduate
Abstract: Inverse limits, topological groups, properties of profinite groups, infinite galois theory.
Language: TR, EN

Title of the course: Homological Algebra
Instructor: Asst. Prof. Ben Walter
Institution: ODTÜ Kıbrıs
Dates: 26 August – 1 September 2019
Prerequisites: Basic knowledge of groups, rings, and modules
Level: Basic knowledge of groups, rings, and modules 
Abstract:
(We will follow Weibel’s homological algebra book.)
Week 1 will be chapters 1—3 (and possibly parts of 4.)
Chain Complexes: definitions, operations, long exact sequences, chain homotopies, mapping cones and cylinders.
Derived Functors: projective and injective resolutions, left and right derived functors, adjoints.
Tor and Ext: Basics, derived functors of inverse limit, universal coefficient theorems.
(Time permitting, we will include a bit of Koszul complexes from chapter 4.)
Language: EN
Textbook or/and course webpage: Weibel, C.  An Introduction to Homological Algebra

Title of the course: Kısmi Türevli Denklemlerde Seçme Konular
Instructor: Assoc. Prof. Erhan Pişkin
Institution: Dicle Ü.
Dates: 26 August – 1 September 2019
Prerequisites: -
Level: Lisans
Abstract: Birinci Mertebeden Kısmi Diferansiyel Denklemler, Yüksek Mertebeden Sabit Katsayılı Kısmi Diferansiyel Denklemler, Dalga Denklemi, D’Alembert Çözümü, Duhamel Prensibi, Değişkenlere Ayırma Yöntemi.   
Language: TR

Title of the course: Ultrafilters and how to use them
Instructor: Asst. Prof. Burak Kaya
Institution: Kadir Has Ü.
Dates: 26 August – 1 September 2019
Prerequisites: No prior knowledge will be needed except some mathematical maturity. For the second half of the course only, some familiarity with algebraic structures and topological concepts are suggested, but not required.
Level: Graduate, advanced undergraduate, beginning Undergraduate
Abstract: In this course, we shall learn about ultrafilters and their applications in mathematics. The first half of the course will cover the basics (i.e. the construction, properties and different types of ultrafilters) and the second half of the course will cover some applications (e.g. the ultraproduct and ultralimit constructions, Stone-Cech compactification of a discrete space.)
Language: TR, EN

Eğitmen: Prof. Dr. Melih Boral
Kurum: -
Tarih: 26 Ağustos – 8 Eylül 2019
Dersin Adı: Sayılar kuramı
İçerik: Bölünebilme, asal sayılar, aritmetiğin temel teoremi, karelerin toplamı olarak sayılar, polinomlar ve cebirsel sayılar, sayılar kuramında ilginç problemler.

Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Ü.
Tarih: 26 Ağustos – 8 Eylül 2019
Dersin Adı: Ağaçlar
İçerik: Bazı kavramlar matematiğin hemen her dalında karşımıza çıkarlar. "Ağaç" kavramı bunlardan biridir. Örneğin, her aşamada iki karardan birini verdiğiniz bir oyun düşünün, bu aslında bir ağaçtır. Ya da bir yol düşünün, her 100 metrede bir üçe ayrılıyor, ya da bazen ikiye bazen üçe ayrılıyor, ama hiç geriye dönmüyor. Bu da bir ağaçtır. Bu derste, ağaçlarla matematiğin çeşitli konuları arasındaki bağı göreceğiz. Reel sayılar, tam sayılar, oyunlar, p-sel sayılar, olasılık, polinomlar içinde ağaç göreceğimiz konulardan bazıları olacak.

Eğitmen: Doç. Dr. Özlem Beyarslan
Kurum: Boğaziçi Ü.
Tarih: 26 Ağustos – 8 Eylül 2019
Dersin Adı: Çizgeler Kuramı
İçerik: Çizgeler teorisinin temel tanımları, güvercin yuvası prensibi, sayma kuralları, çizgelerde tümevarım, düzlemsel çizgeler, çizgeleri boyama, Ramsey sayıları, sonsuz Ramsey teoremi, Hall evlilik teoremi, ağaçlar.

Eğitmen: MSc. Kübra Dölaslan
Kurum: ODTÜ
Tarih: 26 Ağustos – 8 Eylül 2019
Dersin Adı: Problem Saati
İçerik: Lise programındaki derslerde öğretilen kavramlar üzerine problemler sorup birlikte tartışacağız.

Title of the course: An Introduction to Module Theory
Instructor: Asst. Prof. Roghayeh Hafezieh
Institution: Gebze Teknik Ü.
Dates: 2-8 September 2019
Prerequisites: Algebra I
Level: Graduate and advanced undergraduate              
Abstract: We will discuss: Definition of module and submodule, R-module homomorphisms and exact sequences, Direct Product and Direct sums, Hom, and tensor product.
Language: EN

Title of the course: Tensor Products of Modules
Instructor:
Prof. Ali Nesin
Institution:
İstanbul Bilgi Ü.
Dates:
2-8 September 2019
Prerequisites:
Basic module theory
Level:
Graduate, advanced undergraduate
Abstract: As in the title.
Language: TR, EN

Title of the course: Modular numbers and p-adics
Instructor: Assoc. Prof. Özlem Beyarslan
Institution: Boğaziçi Ü.
Dates: 2-8 September 2019
Prerequisites: familiarity with concepts of algebra
Level: Beginning undergraduate, advanced undergraduate, graduate
Abstract: definitions of p-adic numbers in different contexts, Hensel's lemma, p-adic metric and completion.
Language: TR, EN

Title of the course: Introduction to Group and Lie Algebra Homology
Instructor: Asst. Prof. Ben Walter
Institution: ODTÜ Kıbrıs
Dates: 2-8 September 2019
Prerequisites: Basic knowledge of groups, rings, and modules
Level: Basic knowledge of groups, rings, and modules
Abstract: (Ee will follow Weibel’s homological algebra book.)
Week 2 will be chapters 6—7 (with parts of 5 included as needed.)
Group Homology and Cohomology: Definitions and properties, Shapiro’s Lemma, bar resolution, universal central extensions.
Lie Algebra Homology and Cohomology:  Definitions, universal enveloping algebras, H^1 and H_1, H^2 and extensions, Chevalley-Eilenberg Complex, universal central extensions.
(Spectral Sequences:  To be included as needed.)
Language: EN
Textbook or/and course webpage: Weibel, C.  An Introduction to Homological Algebra

Title of the course: ZFC and Vopenka's alternative set theory
Instructor: Dr. Alena Vencovska
Institution: University of Manchester
Dates: 2-8 September 2019
Prerequisites: -
Level: Advanced undergraduate
Abstract: Basics of ZF, axiom of choice and its equivalents, Vopenka's alternative set theory, role of nonstandard analysis within ZFC  and within Vopenka's theory.
Language: EN

Title of the course: Quadratic Forms
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 9-15 September 2019
Prerequisites: Basic algebra and linear algebra.
Level: Graduate, advanced undergraduate
Abstract: We will classify quadratic forms over reals, complexes and finite fields.
Language:
TR, EN

Title of the course: Special Topics in Group Theory
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 16-22 September 2019
Prerequisites: Group theory
Level: Graduate, advanced undergraduate
Abstract: The content of the course will depend on the audience. I have in mind free groups. I also want to show that most finite graphs have no automorphisms except for identity.
Language: TR, EN

Title of the course: Basic Topology
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 16-29 July 2019
Prerequisites: None
Level: Beginning undergraduate, advanced undergraduate, graduate
Abstract: As in the title
Language: TR, EN

Title of the course: Axiom of Choice and Some of Its Consequences
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 23-29 July 2019
Prerequisites: Mathematical maturity and abstract algebra
Level: Graduate, advanced undergraduate
Abstract: As in the title.
Language: TR, EN

Title of the course: Introduction to General Topology
Instructor: Dr. Ahmet Çevik
Institution: JSGA/ODTÜ
Dates: 23-29 September 2019
Prerequisites: Basic logic and sets. Preliminary real analysis is suggested but not required.
Level: Advanced undergraduate
Abstract: This is a standard course on general topology. Topics we shall cover will include metric spaces, open and closed sets, topological spaces, neighborhoods, closure, interior, basis, continous functions, homeomorphism, connectedness, compactness, separation axioms, Tychonoff’s Theorem, Urysohn’s Lemma.
Language: TR, EN