CALCULUS - 1
DAVID ZMIAIKOU
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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 YOU WILL 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.SPACE UNIVERSITY
DATE: 5 Nov - 23 Nov, 2018
DURATION: 3 Weeks
LECTURES: 3 Hours per day
LANGUAGE: English
LOCATION: Barcelona, 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 Marco Baronti, Filippo De Mari, Robertus van der Putten, Irene Venturi (Springer, 2016)
Schaum's Outline of Theory and Problems of Advanced Calculus by Robert C. Wrede, Murray Spiegel, (McGraw-Hill, 2002)