Math010
Discrete Mathematics 1
Faculty
Vladimir Mazin
Msc. Data Science at Harbour.Space University
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
The Basis of Computer Science (CS) theory is built on math theory and the majority of processes in CS are discrete processes. The majority of mathematics in IT is Discrete Mathematics. During this course, we will learn a variety of mathematical topics as a part and in a connection with Discrete Mathematics. All topics will be considered with respect to their connections with other areas and real applications in Computer Science.
Learning highlights
- Understand mathematical and logic statements.
- Understand recursion principles.
- Know basic concepts, terms and notation of discrete mathematics.
- Know the basis of a graph theory and its applications.
- Apply proof technique appropriate to given statement.
- Apply appropriate computational techniques.
Course outline
15 classes
Sets
Subsets, Set Operations, Partitions
Relations
Equivalence Relations, Partial Orderings
Functional relations
Types of Functions, Bijective Functions, Cardinalities of Sets
Quantifier notation, logic
Propositional Logic, Negation, Conjunction, Disjunction, Predicates and Quantifiers
Test I + Review of the week
Test I + Review of the week
Proof techniques
Direct Proof, Proof by Contrapositive, Proof by Cases, Counterexamples
Mathematical Induction
The Principle of Mathematical Induction, Examples of Proofs
Logical functions, Boolean algebra
Logical functions, Boolean algebra
Recursion
Recursive Definitions, Recursive Algorithms
Test II + Review of the week
Test II + Review of the week
Computational techniques
Generating Functions
Graphs I
Graph Terminology, Representing Graphs, Connectivity, Shortest-Path Problems
Graphs II
Planar Graphs, Introduction to Trees, Applications of Trees, Tree Traversal
Tutorial
Tutorial
Final Exam
Final Exam
Prerequisites
Intro to Calculus 2
Feb 01 - Feb 19, 2021
David Zmiaikou
PhD, Lecturer at the Belarusian State University
Algebra 1
Feb 22 - Mar 12, 2021
David Zmiaikou
PhD, Lecturer at the Belarusian State University
Elementary Combinatorics & Probability
Mar 15 - Apr 02, 2021
Evgeniya Korneva
Data Scientist at BOLD
Intro to Programming 3: Python
Apr 12 - Apr 30, 2021
Hossein Yousefi
Co-founder and CTO at Identi
Methodology
Each 3-hour session is a mix of lecture and problem-solving practice with the support of the instructor. Students will solve a variety of mathematical tasks. The lecture parts will be guided by live reasoning using a whiteboard supported by reading materials.
After such a session, students will be given a homework assignment, (±2 hours completion time). Sessions 5 and 10 (tests) are built in the form of a regular 1.5-hour test with computational problems that cover a corresponding week and a 1.5-hour brief review of a week. Session 14 is built in the form of a tutorial with instructions, following which students will solve problems. It is similar to the regular session but without lecturer explanations. Session 15 (final exam) is a big 3-hour test.
Grading
In 2012 with scientific research in Algebra, Vladimir won 1st place at the National contest in Russia, the Intel-Avangard, and became a finalist of the Intel ISEF.
After school, he enrolled for Bachelors at ITMO University for the programme of Applied Math and Programming. During his Bachelor's, he participated in several educational projects: in 2013 he was a coordinator of the national science fair for school students - BalticSEF; in 2014 he was a teacher in the LCME summer school, teaching two courses on maths. In the last years of his Bachelors, Vladimir entered the centre of additional higher education, Computer Science Center, for the programme of Software Engineering. In the end of summer of 2015, he completed a 3-month internship as a Software Developer.
See full profileApply for this course
Discrete Mathematics 1
by Vladimir Mazin
Total hours
45 Hours
Dates
May 03 - May 21, 2021
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.