**CALCULUS - 1**

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.

The objective of the course is to familiarise with basic notions and ideas of calculus: to learn how to calculate the limit of a sequence, how to find a derivative and an integral of a function when it is possible. This course is also a background preparation for studying random variables (in probability).

**SKILLS:**

- Algorithms

- Combinatorics

- Data Analysis

- Discrete Optimization

- Dynamical Systems

- Geometry

- Group Theory

- Software Engineering

ABOUT DAVID

**HARBOUR.SPACE **

WHAT YOUWILL LEARN

**DATE:** 5 Nov - 23 Nov, 2018

**DURATION: **3 Weeks

**LECTURES: **3 Hours per day

**LANGUAGE: **English

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

**COURSE TYPE: **Offline

HARBOUR.SPACEUNIVERSITY

**DATE: **5 Nov** **- 23 Nov, 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**

Trigonometric Functions

**Session 4**

Comparison of Sequences

**Session 3**

Limit of a Sequence

**Session 2**

Introduction to Sequences

**CALCULUS-1**

This course is the first step in calculus, also called mathematical analysis, and serves as a bridge from discrete to continuous. It deals with limits of sequences, and continuity, differentiation and integration of functions.

We will introduce and explore elementary concepts and methods of calculus. For each of them, a geometric interpretation will be given as a key for better understanding.

We will see how these concepts are applied by considering examples and by solving numerous exercises. Among useful results in calculus, we will mention Bolzano-Weierstrass theorem, Rolle’s theorem and mean value theorems.

This course is the first step in calculus, also called mathematical analysis, and serves as a bridge from discrete to continuous. It deals with limits of sequences, and continuity, differentiation and integration of functions.

We will introduce and explore elementary concepts and methods of calculus. For each of them, a geometric interpretation will be given as a key for better understanding.

We will see how these concepts are applied by considering examples and by solving numerous exercises. Among useful results in calculus, we will mention Bolzano-Weierstrass theorem, Rolle’s theorem and mean value theorems.

BIBLIOGRAPHY

Calculus Problems by MarcoBaronti,Filippo De Mari, Robertusvander Putten, Irene Venturi(Springer, 2016)

Schaum's Outline of Theory andProblems of Advanced Calculus byRobert C. Wrede, Murray Spiegel,(McGraw-Hill, 2002)

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