INTRODUCTIONTO CALCULUS 2

YARASLAUZADVORNY

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.

Yaraslau Zadvorny graduated from the Belorussian State University in 2014, majoring in the theory of stability of differential equations. Since then he is a Teaching assistant and a PhD Student at BSU. His research area is the stability of stochastic differential equations. Yaraslau has more than 15 publications. In 2016, he graduated from the School of Data Science (Yandex).

Yaraslau pays a lot of attention to work with talented school students. Since 2017, he is the main trainer of the Belarusian team at the International Tournament of Young Mathematicians. Many of his students became the winners of different competitions, including IMO and ITYM.

- Research / Academic interests:

- Stability of differential equations;

- Probability theory;

- Cryptography.

The main objective of the module is to learn basic techniques of derivative and integral computation.

**SKILLS:**

- Mathematics

- Functions

-Sequences

-Cryptography

-Probability

ABOUT YARASLAU

WHAT YOUWILL LEARN

**DATE:** 27 Jan - 14 Feb, 2020

**DURATION: **3 Weeks

**LECTURES: **3 Hours per day

**LANGUAGE: **English

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

**COURSE TYPE: **Offline

**DATE: **27 Jan - 14 Feb, 2020

**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**

Sequences

**Session 4**

Derivative of a Function

**Session 3**

Functions

**Session 2**

Limit of a Sequence

In this course, we will study the basic definitions and objects of calculus, such as limit, derivative and integral. The course can be also considered as an introduction to the courses of Probability Theory and Computer Science. Thus, a lot of attention will be given to calculation technique.

As a result of the course, students will:

- Understand the basic definitions and operations of calculus, such as sequence, limit, derivative, integral etc.;

- Develop their skills in the calculation of derivatives, integrals etc.;

- Analyze the applications of these objects.

In this course, we will study the basic definitions and objects of calculus, such as limit, derivative and integral. The course can be also considered as an introduction to the courses of Probability Theory and Computer Science. Thus, a lot of attention will be given to calculation technique.

As a result of the course, students will:

- Understand the basic definitions and operations of calculus, such as sequence, limit, derivative, integral etc.;

- Develop their skills in the calculation of derivatives, integrals etc.;

- Analyze the applications of these objects.

REQUIRED READING

Schaum's Outline ofAdvanced Calculus, Second Edition

__By Robert C. Wrede____(McGraw-Hill, 2002)__

Calculus Problems (UNITEXT)

__By Marco Baronti____(Springer, 2016)__

CalculusBy Ron Larson(Cengage Learning, 2017)

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