Köy`de bol bol çadır kuracak yer vardır. Kısıtlı sayıda çadırımız vardır ancak çadırda kalacak katılımcıların çoğunun çadırlarını getireceklerini umuyoruz.
Fiziksel bir engel olmadıkça, katılımcıların Köy`de çamaşır, bulaşık, temizlik, bahçe bakımı, yemek gibi gündelik işlerde yardımcı olacakları varsayılır. Matematik Köyü`nde bir aile ortamı yaratmaya özen gösteriyoruz.
Ayrıntılı Ders Programı
01.Ağu.11 | 08.Ağu.11 | 15.Ağu.11 | 22.Ağu.11 | 29.Ağu.11 | 05.Eyl.11 |
Alexander Borovik | Ali Nesin | David Pierce | Piotr Kowalski | ||
Concrete Group Theory | Topics in Module Theory | Nonstandard Analysis | Topics in Model Theory | ||
Ali Özgür Kişisel | Sonat Süer | Ayhan Günaydın | Ayşe Berkman | Pınar Uğurlu | |
Cebirsel Geometri | Infinitesimal Numbers | Intr. to Algebraic Geometry | Geometric Algebra | Klasik Gruplar | |
E. Mehmet Kıral | Özlem Beyarslan | Özlem Beyarslan and Martin Hils | |||
Hecke’s theory of modular forms | Introduction to Representation Theory | Valued Fields | |||
Ali Nesin | Ali Nesin | Ali Nesin | Alp Eden | Oleg Belegradek | Selçuk Demir |
Some Advanced Mathematical Ideas | Quadratic Reciprocity and more | Gauss and Jacobi Sums | Dinamik Sistemler | Nullstellensatz and Model Theory | Topics in Harmonic Analysis |
*** Kamp koordinatörlerimizden Prof. Dr. Haluk Oral 1 – 14 Ağustos tarihleri arasında Nesin Matematik Köyü`nde olacaktır. İlk gün kampı tanıtıcı bir açılış konuşması verecektir. Ve kamp boyunca programı takip edecektir.
Başlık: Concrete Group Theory
Eğitmen: Prof. Alexandre Borovik
Kurum: Manchester University
Tarih: 1-21 Ağustos 2011
Önkoşul: Linear algebra, basic group theory
Seviye: Advanced undergraduate and graduate
İçerik:
Stalling`s graph of a subgroup. Algorithms for free groups.
Başlık: Cebirsel Geometri
Eğitmen: Assoc. Prof. Ali Özgür Kişisel
Kurum: Middle East Technical University, Northern Cyprus Campus
Tarih: 1-7 Ağustos 2011
Önkoşul: Abstract algebra. Complex analysis and a geometry / topology course would be beneficial.
Seviye: Advanced undergraduate and graduate
İçerik: Affine and projective algebraic curves, classical constructions, Riemann surfaces, degree-genus formula, Bezout`s theorem, differentials and Riemann-Roch, enumerative problems, tropical algebraic curves.
Başlık: Infinitesimal Numbers
Eğitmen: Dr. Sonat Süer
Kurum: İstanbul Bilgi Üniversitesi
Tarih: 8-21 Ağustos 2011
Önkoşul: Basic analysis, definition of a smooth manifold. Some familiarity with logic would be helpful but it is not necessary.
Seviye: Advanced undergraduate and graduate
İçerik: The course is a very short introduction to three very different approaches to the idea of infinitely small number, namely surreal numbers, nonstandart analysis and smooth infinitesimal analysis. The course will cover only the construction and basic properties of infinitesimals in each of these frameworks. Here is a rough syllabus:
Başlık: Hecke`s theory of modular forms
Eğitmen: MSc. Eren Mehmet Kıral
Kurum: Brown University
Tarih: 1-7 Ağustos 2011
Önkoşul: Complex analysis, linear algebra including knowledge of inner product spaces, self adjoint operators. Some Fourier analysis; in connection with the Riemann zeta function, Poisson summation formula is required, but it is absolutely acceptable if one is only willing to accept the statement of the formula.
Seviye: Advanced undergraduate and graduate.
İçerik: We will investigate modular forms, their L functions; and the reciprocal relation between modular substitutions and Hecke operators, and functional equations of the L function and their Euler product expansions. We will also try to shed some light on the number theoretic importance of the theory of modular forms, and fit the Riemann zeta function and the Dirichlet L functions into the theory.
Başlık: Inroduction to Representation Theory
Eğitmen: Dr. Özlem Beyarslan
Kurum: Boğaziçi Üniversitesi
Tarih: 8-21 Ağustos 2011
Önkoşul: Graduate
Seviye: Lineer cebir, ve temel cebir bilgisi
İçerik: FG-modules submodules homomorphisms, Group algebras, Maschke`s theorem, Schur`s lemma, Irreducible modules and group algebras, Group characters, Character tables, Tensor products, Induced modules and characters, Characters of some p-groups.
Başlık: Some Advanced Mathematical Ideas
Eğitmen: Prof. Dr. Ali Nesin
Kurum: İstanbul Bilgi Üniversitesi
Tarih: 1-7 Ağustos 2011
Önkoşul: —
Seviye: Graduate and advance graduate
İçerik: A few independent topics:
1) Direct and inverse limits and their relationship.
2) Tensor product.
3) Ideal, filter, ultrafilter, ultraproduct and nonstandard arithmetic and analysis.
4) Category theory, products and free objects.
Başlık: Quadratic Reciprocity and More
Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Üniversitesi
Tarih: 8-14 Ağustos 2011
Önkoşul: Basic field theory and group theory.
Seviye: Undergraduate and graduate
İçerik: Quadratic residue, Legendre symbol, Law of quadratc reciprocity, quadratic Gauss sums.
Başlık: Gauss and Jacobi Sums
Eğitmen: Prof. Ali Nesin
Kurum: İstanbul Bilgi Üniversitesi
Tarih: 15-21 Ağustos 2011
Önkoşul: Basic algebra.
Seviye: Undergraduate and graduate
İçerik: Multiplicative characters, Gauss sums, Jacobi sums, the equation x^n+ y^n = 1 in F_n. Generalizations.
Başlık: Topics in Module Theory
Eğitmen: Prof. Dr. Ali Nesin
Kurum: İstanbul Bilgi Üniversitesi
Tarih: 22-28 Ağustos 2011
Önkoşul: —–
Seviye: Undergraduate and graduate
İçerik:
1) Tensor products of modules.
2) Free modules: Invariant basis number. Stable finiteness. The rank condition.
The strong rank condition.
3) Projective modules.
4) (Time permitting) injective modules.
Başlık: Nonstandard Analysis
Eğitmen: Doç. Dr. David Pierce
Kurum: ODTÜ
Tarih: 29 Ağustos – 4 Eylül 2011
Önkoşul: Knowledge of epsilon-delta proofs in calculus, and of algebra (for example, that the quotient of a ring by a maximal ideal is a field)
Seviye: Advanced undergrad and graduate.
İçerik: A distinction between calculus as a computational tool, and analysis as a rigorous mathematical discipline, was recognized by Archimedes. Calculus as we know it today was developed in the 17th century by means of infinitesimals, but the notion of an infinitesimal was not then made rigorous. In the 19th century, calculus was made rigorous by means of limits: thus began analysis. In 1960, Abraham Robinson used the tools of mathematical logic to make the notion of infinitesimals rigorous: this begins non-standard analysis. This course will review some of the work of Archimedes, along with Dedekind`s construction of the real numbers, before constructing the “non-standard real numbers”—among which are the infinitesimals—and proving theorems with them.
Başlık: Topics in model theory
Eğitmen: Dr. Piotr Kowalski
Kurum: Uniwersytetu Wroclawskiego
Tarih: 5-11 Eylül 2011
Önkoşul: Basic knowledge in algebra and analysis
Seviye: Advanced undergraduate and graduate.
İçerik: Languages, structures, types, compactness theorem, elementary equivalence, complete theories, categoricity, quantifier elimination, Morley rank, strongly minimal theories, ACF, o-minimal theories, RCF, differentialfields, time permitting applications to diophantine geometry.
Başlık: Introduction to Algebraic Geometry
Eğitmen: Dr. Ayhan Günaydın
Kurum: Universidade de Lisboa
Tarih: 22-28 Ağustos 2011
Önkoşul: A good background in algebra, mostly commutative algebra
Seviye: Advanced undergraduate and graduate.
İçerik: We shall start with a thorough study of basic notion of algebraic geometry; such as affine and projective varieities and maps between them. Then in the remaining time, we shall study more involved topics as sheaves and schemes.
Başlık: Geometric Algebra
Eğitmen: Doç. Dr. Ayşe Berkman
Kurum: ODTÜ
Tarih: 29 Ağustos – 4 Eylül 2011
Önkoşul: A course in linear algebra and a course in abstract algebra. Seviye: : Advanced undergraduate/graduate İçerik: Affine and projective geometries. Bilinear forms. Symplectic and orthogonal geometries. Their isometries.
Başlık: Classical groups
Eğitmen: Dr. Pınar Uğurlu
Kurum: İstanbul Bilgi Üniversitesi
Tarih: 5-11 Eylül 2011
Önkoşul: Linear algebra and basic group theory.
Seviye: Graduate.
İçerik: Linear and projective groups, bilinear forms, symplectic groups, symmetric and quadratic forms, orthogonal groups, hermitian forms and unitary groups.
Başlık: Valued Fields
Eğitmen: Dr. Özlem Beyarslan, Assoc. Prof. Martin Hils
Kurum: Boğaziçi Üniversitesi,Université Paris 7
Tarih: 22 Ağustos – 11 Eylül 2011
Önkoşul: En az bir cebir dersi almış olmak gerekir.
Seviye: Graduate
İçerik: Absolute values, Valuations, Extensions of valuations, Henselian fields, Applications of valuation theory
Başlık: Dinamik Sistemler
Eğitmen: Prof. Dr. Alp Eden
Kurum: Boğaziçi Üniversitesi
Tarih: 22-28 Ağustos 2011
Önkoşul: Hilbert Uzayları ve Linear Operator Teorisi hakkında temel bilgiler
Seviye: Lisansüstü birinci sınıf
İçerik: This course will basically cover Chapters 8-10 from the book Exponential Attractors for Dissipative Evolution Equations”with supplementary materials from various papers. Its main aim is to introduce the notions of Inertial Manifolds, Exponential Attractors and the induced finite dimensional dynamics on them through the Hölder-Mane Projections. These will be done on a class of abstract dissipative first-order evolution equations. I will first show the existence of Inertial manifolds with the help of spectral barriers as exposed in a paper of Constantin, this will take us around two lectures. Then I will mention a contruction of exponential attractors as was done by Eden et. al. and improved in Babin and Nicolaenko. Finally, I will expose Chapter 10 from the above mentioned book with ramifications as suggested by Robinson and co-workers.
Başlık: Nullstellensatz vs model theory
Eğitmen: Prof. Oleg Belagradek
Kurum: İstanbul Bilgi Üniversitesi
Tarih: 29 Ağustos – 4 Eylül 2011
Önkoşul: solid course of basic algebra including elements of field theory
Seviye: Graduate and senior undergraduate
İçerik: I am going to present Hilbert`s Nullstellensatz in the classical form and for the case of the real field, and to discuss it from the model theoretic point of view.
Başlık: Topics in Harmonic Analysis
Eğitmen: Doç. Dr. Selçuk Demir
Kurum: İstanbul Bilgi Üniversitesi
Tarih: 5-18 Eylül 2011
Önkoşul: Reel analiz ve fonksiyonel analiz
Seviye: Graduate and advance graduate
İçerik: Fourier series, fourier integrals, fourier transform, based on examples: On the circle, on the Euclidean Space, on the sphere and on the Poincare Upper Half Plane