Math105
Calculus 1
Faculty
Serhii Denysov
Senior algorithms R&D at drawer.ai, Programming and math university teacher.
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
In this course, students will learn the basic concepts, techniques, and applications of continuous higher mathematics — sequences and their properties, limits, functions and their properties, as well as limits and derivatives with basic applications. The idea of the integral (both indefinite and definite) will also be introduced, together with basic integration techniques and applications. Along the way, students will practise rigorous and abstract reasoning and thinking, preparing them for subsequent mathematics and data science courses. The concept of asymptotic estimates for sequences and functions will also be introduced, as it relates to similar concepts widely used in programming and algorithmic fields.
Learning highlights
- Learn to deal with infinity, both in sequences (countable infinity) and in functions — continuity and limits.
- Improve your mathematical reasoning and basic proof techniques.
- Learn the concepts of differentiation and integration, and understand the applied aspects of these fields of mathematics.
Course outline
15 classes
Session 1
Intro to calculus and mathematical analysis. Math refresher. Dealing with mathematical equalities and inequalities.
Session 2
Sequences. Tail / eventually properties. Proving asymptotic equalities and inequalities with mathematical induction.
Session 3
Limit of a sequence. Finding limits and proving related properties.
Session 4
Squeeze theorem. Practice with sequence limits.
Session 5
Function. Informal and formal definition. Monotonicity, convexity and other properties. Inverse function.
Session 6
Function limit. Continuity. Intermediate value theorem. O and o notation for functions. Asymptotic behavior near zero.
Session 7
Function derivative. Intuition and applications. Mean value and Rolle's theorem. Chain rule.
Session 8
L’hopital rule. Practice with function limits, derivatives, properties and graphs.
Session 9
Midterm exam
Session 10
Taylor series. Uniform continuity. Lipschitz property. Contraction.
Session 11
Integration. Antiderivative. Integration by parts. Integration practice.
Session 12
Definite integral as area under the curve. Rieman definition of integral. Fundamental theorem of calculus. Average value theorem. Practice with integral sums.
Session 13
Definite integration practice. Integral inequalities practice.
Session 14
Recap, Q&A, bonus topics.
Session 15
Final exam
Prerequisites
Basic algebraic literacy – solving one-dimensional equations, inequalities; working with fractions, absolute values, summation, and school-level elementary functions (sin, cos, ln, exp).
Basic geometric literacy — angles, distances, the Cartesian coordinate plane, circles, and triangles.
Understanding of basic mathematical notation.
Basic Python programming skills for numerical experiments.
Methodology
A mixed format, in which lectures are interleaved with practical demonstrations and discussions, involving students in solving problems on the whiteboard or conducting numerical experiments.
Grading
Serhii has worked in the software engineering industry in different positions for many years. Roles included software developer, system architect, IT consultant, project manager and CTO. He is also an experienced educator and is always glad to help students learn how to start having fun with programming and math and become top-level software developers or R&D engineers.
He has taken part in a long row of business automation projects for different businesses, with many small and several big projects, such as one of the biggest outdoor advertising agency in Ukraine and a country-wide software cash registers company, processing millions of transactions per day. Now he is a senior algorithms R&D in a highly dynamic startup drawer.ai.
See full profileApply for this course
Calculus 1
by Serhii Denysov
Total hours
45 Hours
Dates
Dec 01 - Dec 19, 2025
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.