FOUNDATIONSOFMATHEMATICALREASONING

DAVIDZMIAIKOU

Combinatorics and graph theory lay at the heart of discrete mathematics and computer science. In the course, we begin with a brief review of the fundamentals of combinatorics---counting, permutations, binomial coefficients, and the pigeonhole principle---and then devote most of the course to the fundamentals of graph theory. We cover the most common definitions and ideas of graph theory, proving important theorems and introducing important algorithms, but mostly aiming to simply establish the common language of discrete mathematics and computer science.

Several years ago, David Zmiaikou obtained his Ph.D. degree at the University Paris-Sud (Orsay) under the supervision of Professor Jean-Christophe Yoccoz. After that, he visited the mathematical institute IMPA in Rio de Janeiro thanks to the Balzan research project of Professor Jacob Palis.

As a part of David's European Post-Doctoral Institute (EPDI) fellowship, he worked at:

**• **Erwin Schrödinger Institute for Mathematical Physics, Vienna, Austria

**• **Institute for Mathematical Research, Zürich, Switzerland

**• **Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France

**• **Max Planck Institute for Mathematics Bonn, Germany

Afterwards, David did postdoctoral research in DNA analysis at the Wellcome Trust Sanger Institute in the United Kingdom.

One of the goals of the course is to provide necessary background and tools for studying further more profound courses.

More importantly, students will learn how to approach a large variety of mathematical problems by reasoning logically and abstractly.

**SKILLS:**

- Algorithms

- Combinatorics

- Data Analysis

- Discrete Optimization

- Dynamical Systems

- Geometry

- Group Theory

- Software Engineering

ABOUT DAVID

**HARBOUR.SPACE **

WHAT YOUWILL LEARN

**DATE:** 15 Oct - 02 Nov, 2018

**DURATION: **3 Weeks

**LECTURES: **3 Hours per day

**LANGUAGE: **English

**LOCATION: **__Barcelona, Harbour.Space Campus__

**COURSE TYPE: **Offline

HARBOUR.SPACEUNIVERSITY

**DATE: **15 Oct** **- 26 Oct, 2018

**DURATION: **3 Weeks

**LECTURES: **3 Hours per day

**LANGUAGE: **English

**LOCATION: **__B____arcelona, Harbour.Space Campus__

**COURSE TYPE: **Offline

All rights reserved. 2018

COURSE OUTLINE

**Session 1**

Elements of Logic

**Session 4**

Functions: Basic Terminology

**Session 3**

Numbers: Real Line

**Session 2**

Sets: Operations and Relations

FOUNDATIONSOFMATHEMATICALREASONING

This course is an introduction to mathematical thinking and techniques of proof. During the course, basic notions and notations will be given. We will encounter sets, relations, functions, real and complex numbers, modular arithmetic, and polynomials.

In order to study this subjects efficiently and to be able to obtain exact results, students will be exposed to different techniques of formal proof. These will in particular be mathematical induction, arguing by contradiction, equivalence and pigeonhole principle.

Why is there such an emphasis on digital marketing in business today? How has digital marketing changed the relationship between customers and businesses? What’s the relationship between digital marketing and content marketing?

These are the foundational questions we’ll dig into during this two-week session.Course projects may become a building block for students’ Capstone Project / product

This course is required for all digital marketing students, both graduate and undergraduate

BIBLIOGRAPHY

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