Bootcamp 8 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Bootcamp 8 (of 8)

Lecturer: Jan Hubička

Date: Wednesday October 12, 2016.

Main Topics: Ramsey lifts, Classification results, Tournaments, Digraphs, Permutations, unary functions, Steiner Systems, Dual Ramsey, Graham-Rothschild.

Definitions: Digraph, Tournament, Interposition, \text{CSP}(G) , Strong substructure, unary function, Steiner System

Bootcamp 1 – Bootcamp 2 – Bootcamp 3 – Bootcamp 4 – Bootcamp 5 – Bootcamp 6 – Bootcamp 7 – Bootcamp 8

Note: The material here is meant as an overview, so many details are missing.
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Functions on Homogeneous Ramsey Structures 3 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Functions on Homogeneous Ramsey Structures 3 (of 3).

Lecturer: Michael Pinsker.

Date: Friday October 14, 2016.

Main Topics: Proof of Ramsey claim for canonical functions, Thomas’ Theorem for the Rado Graph, Open questions

Definitions: No new definitions

Lecture 1 – Lecture 2 – Lecture 3

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Bootcamp 7 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Bootcamp 7 (of 8)

Lecturer: Jan Hubička

Date: Monday October 10, 2016.

Main Topics: “Correct” definition of Ramsey expansion, Ramsey lifts/expansions of graphs, Ramsey lifts/expansions of posets.

Definitions: Precompact expansion, Expansion property, Free Amalgamation, strong type, equivalence formula, equivalence closure, interpretation in a model.

Bootcamp 1 – Bootcamp 2 – Bootcamp 3 – Bootcamp 4 – Bootcamp 5 – Bootcamp 6 – Bootcamp 7 – Bootcamp 8

INCOMPLETE: One dimensional proof of t copies of K_\omega , \omega copies of K_\omega .

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Functions on Homogeneous Ramsey Structures 2 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Special thanks. Thank you to Michael Kompatscher for all his feedback and helpful comments.

Title: Functions on Homogeneous Ramsey Structures 2 (of 3).

Lecturer: Michael Pinsker.

Date: Friday October 7, 2016.

Main Topics: Equivalent notions of \omega -categorical, Proof of Cameron’s Theorem, Proof of canonical-Ramsey.

Definitions:No new ones.

Lecture 1 – Lecture 2 – Lecture 3

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Functions on Homogeneous Ramsey Structures 1 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Special thanks. Thank you to Michael Kompatscher for helpful fixes and feedback.

Title: Functions on Homogeneous Ramsey Structures 1 (of 3)

Lecturer: Michael Pinsker

Date: Wednesday October 5, 2016.

Main Topics: Canonical functions, \omega -categorical structures, Automorphisms vs preserving types.

Definitions:[S]^n , type, theory, canonical function, \omega -categorical structure, pointwise convergence.

Lecture 1 – Lecture 2 – Lecture 3
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Bootcamp 6 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Bootcamp (6 of 6)

Lecturer: Jaroslav Nesetril

Date: Monday October 3, 2016.

Main Topics: Other applications of the “product argument”, Chain-Ramsey for Posets, Proof of edge-Ramsey for Graphs, Proof of Hales-Jewett

Definitions: Structural pigeonhole principle, Poset, Graph product, Combinatorial line

Bootcamp 1 – Bootcamp 2 – Bootcamp 3 – Bootcamp 4 – Bootcamp 5 – Bootcamp 6
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Bootcamp 5 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Bootcamp 5 (of 8)

Lecturer: Jan Hubička

Date: Friday September 30, 2016.

Main Topics: Rado Graph, Fraïssé’s Theorem, Examples of Fraïssé classes, Ramsey implies Amalgamation, Lifts and Reducts, Ramsey classes have linear orders

Definitions: Extension Property, Ultrahomogeneous, Universal, \text{Age}(A) , Fraïssé class, irreducible structure, Lifts/Expansions and Shadows/reducts.

Bootcamp 1 – Bootcamp 2 – Bootcamp 3 – Bootcamp 4 – Bootcamp 5 – Bootcamp 6 – Bootcamp 7 – Bootcamp 8

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Bootcamp 4 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Special thanks to Matěj Konečný for helpful feedback.

Title: Bootcamp 4 (of 8)

Lecturer: Jaroslav Nešetřil

Date: Monday September 26, 2016.

Main Topics: Graphs have the ordering property, Ordered Edge-Ramsey implies Ordering property, Graphs are not Ramsey, Amalgamation for Ramsey classes, the product argument, Hilbert’s Theorem.

Definitions: Joint Embedding Property, Amalgamation Property, statement of Hilbert’s Theorem.

Bootcamp 1 – Bootcamp 2 – Bootcamp 3 – Bootcamp 4 – Bootcamp 5 – Bootcamp 6 – Bootcamp 7 – Bootcamp 8

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Bootcamp 3 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Bootcamp (3 of 6)

Lecturer: Jaroslav Nešetřil

Date: Friday September 23, 2016.

Main Topics: Point Ramsey for graphs, \langle A,B,C \rangle hypergraphs.

Definitions: Ramsey property for finite structures, Ramsey Class, point-Ramsey, edge-Ramsey, \langle A,B,C \rangle hypergraphs, Chromatic number, Ordering Property.

Bootcamp 1 – Bootcamp 2 – Bootcamp 3 – Bootcamp 4 – Bootcamp 5 – Bootcamp 6 – Bootcamp 7

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Stepping up your Math Game – 35 Summer Projects for Post-Secondary Math Students

Build your math muscles!

This summer invest in your math education.

Undergraduate students often ask me for advice for how to improve themselves as mathematicians. There are many answers to this question: you can focus on learning new mathematics, you can work on your programming skills, you can improve your career prospects by working on professional development, …

This post is the result of many conversations and coffees with undergrads; It is the advice that I would have given myself as a second-year undergrad at the University of Winnipeg. These 35 projects will also provide necessary skills for completing a Ph.D. in Mathematics and will increase your employability.

Some of these projects will take an afternoon (“Learn how to make a bibliography in LaTeX”) and some might take a month (“Make a Predator-Prey Visualizer”). There is no time limit and no test, so take your time and make it your own.

Table of Contents

  1. Math Skills
  2. Reading
  3. Math Projects
  4. Teaching
  5. Professional Development
  6. Other Skills

[B] Beginners

Some projects are marked with a [B]. These are especially well-suited for beginners.

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