IT landscape, AI and Math, Educational pathways

AI in School Math and IT

aleksandr.avdiushenko@jetbrains.com

This slides at avalur.github.io

Let's start with an example

Prove that the dashed lines pass through one common point

Mistake!

Mistake!

This is amazingly correct!

Wikipedia article "Malfatti_circles"
Main steps of the proof
1. Homotheties for each pair of circles give us centers $A_2, B_2, C_2$
2. These three homotheties centers lie on one line by Monge's theorem
3. The final step is Desargues's theorem for triangles $ABC$ and $A_1B_1C_1$
And GPT o3 is even smarter...

The same in coding

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1. How many years does a bachelor's degree CS program in Europe typically take?

A. 3 years

B. 3+1 years

C. 4 years

D. 5 years

2. In what year of study is the course on ML usually?

A. First year

B. Second year

C. Third year

D. ML is not among the mandatory courses

Next up, we have a question about the typical year of study when students encounter Machine Learning courses in their bachelor's programs.
The question is: In what year of study is the course on Machine Learning usually offered?
Your options are: A. First year B. Second year C. Third year D. Machine Learning is not among the mandatory courses
Please take a moment to consider your answer and click on the option you think is correct. This question is designed to test your understanding of how Machine Learning fits into the broader computer science curriculum across various universities.
Unfortunately, the correct answer is D. Machine Learning is not among the mandatory courses in the first three years of study.

3. Where is "Supervision for teaching thought"?

A. University of Oxford

B. ETH Zurich

C. University of Cambridge

D. Imperial College London

E. Technical University of Munich TUM

F. École Polytechnique Fédérale de Lausanne

Now, let's move on to the next question, which is about a unique feature of a specific university's Computer Science program.
The question is: Where is the concept of "Supervision for teaching thought" introduced?
You have several options to choose from: A. University of Oxford B. ETH Zurich C. University of Cambridge D. Imperial College London E. Technical University of Munich TUM F. École Polytechnique Fédérale de Lausanne
Take a moment to think about your answer and click on the option you believe is correct. This question will test your knowledge of the distinctive teaching methods employed by different universities in their Computer Science programs.
The correct answers are A. University of Oxford and C. University of Cambridge. Both of these institutions offer the concept of "Supervision for teaching thought" as part of their programs.

4. Which bachelor's degree CS program has a physics semester course?

A. University of Oxford

B. ETH Zurich

C. Technical University of Munich TUM

D. École Polytechnique Fédérale de Lausanne

5. What is the maximum number of mandatory courses in the first year of study?

A. 8

B. 10

C. 12

D. 14

Our next quiz question is about the number of mandatory courses that students typically take in the first year of a Computer Science program.
The question is: What is the maximum number of mandatory courses in the first year of study?
You have four options to choose from: A. 8 B. 10 C. 12 D. 14
Take a moment to consider your answer and click on the option you believe is correct. This question will test your knowledge of the structure and requirements of Computer Science programs in their initial year of study.
The correct answer is C. 12, which represents the maximum number of mandatory courses that students typically take in the first year of a Computer Science program.

6. Where can you work for a company for a year during your bachelor’s degree and return to finish your studies?

A. ETH Zurich

B. University College London

C. Imperial College London

D. Technical University of Munich TUM

Common features of top European CS bachelor's degrees

3 years of studying
About a third of electives
At least one semester project
Supervision for teaching thought
Little Math
Optional Machine Learning

Important note

In many ways, Supervision is a substitute for checking weekly assignments. And often there are only exams in core subjects at the end of the first year.

For instance, at Oxford the first year is really special. Students have to pass 4 combined exams in 9 subjects to get into the second year of study. Exams happen at the end of the year (not the semester):

Functional Programming, Design and Analysis of Algorithms
Imperative Programming
Discrete Mathematics, Probability, and Continuous Mathematics
Digital Systems, Linear Algebra and Introduction to Formal Proof

Let's go on, and here I want to emphasize the importance of Supervision.
In some universities, Supervision serves as a substitute for the traditional method of weekly assignment checking. Instead of regular assessments, students often only face exams in their core subjects at the end of the first year.
For example, at Oxford, the first year is exceptionally rigorous. Students must pass four combined exams covering nine subjects to progress to the second year. These exams are held at the end of the year, rather than each semester.
Here are the subjects included in these exams: 1. Functional Programming, and Design and Analysis of Algorithms 2. Imperative Programming 3. Discrete Mathematics, Probability, and Continuous Mathematics 4. Digital Systems, Linear Algebra, and Introduction to Formal Proof This system ensures that students have a comprehensive understanding of each subject before they are tested, allowing for a more in-depth and integrated learning experience.

Types of practical projects for the students

Individual project — maybe part of the course (UCL, Oxford)
Group project — often from industry partner (TUM, Ecole, Oxford, Delft)
Research project — usually the result is Thesis (all, except Ecole)

Let's discuss the types of practical projects that students can engage in during their studies.
Firstly, we have **Individual Projects**. These are often integrated into the course curriculum and allow students to apply the concepts they've learned in a more focused and personalized manner. Universities like UCL and Oxford frequently incorporate individual projects into their courses.
Next, there are **Group Projects**. These projects are typically collaborative efforts, often involving partnerships with industry. They provide students with the opportunity to work in teams, simulating real-world scenarios and fostering skills in teamwork and communication. Institutions such as TUM, Ecole Polytechnique, Oxford, and Delft are known for facilitating group projects, often with input from industry partners.
Lastly, we have **Research Projects**. These projects usually culminate in a thesis and are mandatory in most universities, except for Ecole Polytechnique. Research projects are critical for students interested in deepening their knowledge and contributing original findings to their field of study.
Each type of project offers unique benefits and learning experiences, ensuring that students are well-prepared for their future careers, whether in academia, industry, or research.

Almost Perfect Bachelor's Program in Cyprus: Year 1

Quarter 1	Quarter 3	Quarter 4
Functions of One Variable, Derivatives	Integral Calculus and Functions of Many Variables
Algebra 1	Algebra 2
Logic and Combinatorics	Discrete Probability and Graph Theory
CS Basics with Python	Algorithms and Data Structures 1
Programming Basics with C	Programming Paradigms	Individual Project

Year 2

Quarter 1	Quarter 3	Quarter 4
Continuous Probability Theory	Mathematical Statistics
Fundamentals of Machine Learning	Advanced Machine Learning
Algorithms and Data Structures 2	Operating Systems Development
Computer Architecture	Language for Science	Tech management
Projects in Kotlin	Group project

Year 3

Quarter 1	Quarter 2	Quarter 3	Quarter 4
Theoretical computer science		Math Elective
Compilers		Robotics and Computer Vision
Database Systems		Electives
Electives		Electives
Group project		Group project

Year 4 (final)

Quarter 1	Quarter 2	Quarter 3	Quarter 4
Electives		Electives
Electives		Electives
Electives		Electives
Research Methods		Thesis 2
Thesis 1		Thesis 2

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Holywar topics for discussions

How much math is necessary for a bachelor's degree in CS? Is it 3 courses or 10 out of 30?
Do we need to teach students team work, ethics, and soft skills on special courses?
An ideal portrait for graduate of a bachelor's degree in CS?

Finally, let's dive into some of the hotly debated topics in the field of computer science education. These are often referred to as 'holy war' topics because of the strong opinions they evoke.
Firstly, we have the question: **How much math is necessary for a bachelor's degree in computer science?** Should it be limited to around 3 courses, or should it be as many as 10 out of a total of 30? This debate centers around the balance between theoretical knowledge and practical skills. Some argue that a strong foundation in mathematics is essential for understanding complex algorithms and systems, while others believe that too much emphasis on math can detract from the hands-on learning of programming and software development.
Secondly, there's the discussion on whether **we need to teach students teamwork, ethics, and soft skills in dedicated courses**. In the tech industry, collaboration and ethical considerations are increasingly important. However, integrating these soft skills into a curriculum traditionally focused on technical abilities remains controversial. Should these skills be taught as separate courses, or should they be embedded within technical courses?
Lastly, we contemplate the **ideal portrait of a graduate with a bachelor's degree in computer science**. What attributes and skills should they possess? This touches on both the depth and breadth of knowledge, the balance between theoretical and practical skills, and the importance of personal and professional development.
Thank you for your attention. I'm open to any further questions.