<![CDATA[MKLab - COURSES]]> https://mklab.gr/ Wed, 29 Jul 2026 08:23:44 +0000 MyBB <![CDATA[MIT Godel Escher Bach]]> https://mklab.gr/showthread.php?tid=1302 Sat, 25 Jul 2026 19:19:39 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1302
Summary

The MIT OpenCourseWare seminar “Gödel, Escher, Bach” is an interdisciplinary discussion-based course built around Douglas Hofstadter’s Pulitzer Prize-winning book Gödel, Escher, Bach: An Eternal Golden Braid. It explores the deep connections between mathematics, logic, art, music, language, computer science, philosophy, and cognitive science, asking fundamental questions about intelligence, consciousness, recursion, and whether machines can truly think. Rather than focusing solely on Gödel, Escher, and Bach as historical figures, the course uses their ideas to uncover common patterns that appear across seemingly unrelated disciplines. Students read the book carefully, solve its puzzles, analyse its dialogues, and appreciate the Bach compositions that inspired many of its themes.

 The seminar meets twice a week in a small, discussion-oriented format, encouraging active participation instead of traditional lectures. Assessment is simple and pass/fail, based on attendance, completing the assigned readings, participating in discussions, and finishing occasional assignments. The course is designed not only to teach technical concepts but also to develop creative, interdisciplinary thinking and a deeper appreciation of how complex systems, self-reference, and symbolic reasoning shape both human minds and artificial intelligence. 

VIDEO LECTURES

COURSE PAGE]]>
Summary

The MIT OpenCourseWare seminar “Gödel, Escher, Bach” is an interdisciplinary discussion-based course built around Douglas Hofstadter’s Pulitzer Prize-winning book Gödel, Escher, Bach: An Eternal Golden Braid. It explores the deep connections between mathematics, logic, art, music, language, computer science, philosophy, and cognitive science, asking fundamental questions about intelligence, consciousness, recursion, and whether machines can truly think. Rather than focusing solely on Gödel, Escher, and Bach as historical figures, the course uses their ideas to uncover common patterns that appear across seemingly unrelated disciplines. Students read the book carefully, solve its puzzles, analyse its dialogues, and appreciate the Bach compositions that inspired many of its themes.

 The seminar meets twice a week in a small, discussion-oriented format, encouraging active participation instead of traditional lectures. Assessment is simple and pass/fail, based on attendance, completing the assigned readings, participating in discussions, and finishing occasional assignments. The course is designed not only to teach technical concepts but also to develop creative, interdisciplinary thinking and a deeper appreciation of how complex systems, self-reference, and symbolic reasoning shape both human minds and artificial intelligence. 

VIDEO LECTURES

COURSE PAGE]]> <![CDATA[Introduction to Mathematical Thinking [UC Berkeley]]]> https://mklab.gr/showthread.php?tid=1167 Fri, 17 Jul 2026 16:32:13 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1167 Introduction to Mathematical Thinking
by  [UC Berkeley]

Summary

The Introduction to Mathematical Thinking (IMT) DeCal was a student-led course at UC Berkeley created to help students develop the kind of logical reasoning and mathematical maturity needed for advanced mathematics and computer science. Rather than focusing on calculations, the course teaches students how to read mathematical notation, understand precise definitions, construct rigorous proofs, and recognize sound logical arguments.

 Topics include proof techniques, induction, number theory, modular arithmetic, sets, functions, combinatorics, graph theory, probability, and other foundational ideas that form the backbone of higher mathematics. Although the course ended after Spring 2019, all of its lectures, notes, videos, homework, and learning materials remain freely available online, making it a valuable self-study resource for anyone interested in strengthening their mathematical thinking. Whether preparing for university-level mathematics or simply wanting to think more clearly and rigorously, the IMT DeCal provides an accessible and well-structured introduction to the mindset of a mathematician.


COURSE]]> Introduction to Mathematical Thinking
by  [UC Berkeley]

Summary

The Introduction to Mathematical Thinking (IMT) DeCal was a student-led course at UC Berkeley created to help students develop the kind of logical reasoning and mathematical maturity needed for advanced mathematics and computer science. Rather than focusing on calculations, the course teaches students how to read mathematical notation, understand precise definitions, construct rigorous proofs, and recognize sound logical arguments.

 Topics include proof techniques, induction, number theory, modular arithmetic, sets, functions, combinatorics, graph theory, probability, and other foundational ideas that form the backbone of higher mathematics. Although the course ended after Spring 2019, all of its lectures, notes, videos, homework, and learning materials remain freely available online, making it a valuable self-study resource for anyone interested in strengthening their mathematical thinking. Whether preparing for university-level mathematics or simply wanting to think more clearly and rigorously, the IMT DeCal provides an accessible and well-structured introduction to the mindset of a mathematician.


COURSE]]> <![CDATA[Essence of calculus [3Blue1Brown]]]> https://mklab.gr/showthread.php?tid=1129 Wed, 15 Jul 2026 22:46:38 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1129 by [3Blue1Brown]

Summary

The Essence of Linear Algebra playlist by 3Blue1Brown transforms what is often considered one of the most intimidating areas of mathematics into an intuitive and visually engaging experience. Rather than focusing on memorizing formulas or performing lengthy calculations, the series explains the geometric ideas behind vectors, matrices, and linear transformations, helping viewers understand what these concepts actually represent. As the lessons progress, it explores topics such as matrix multiplication, determinants, inverses, dot and cross products, changes of basis, eigenvectors, eigenvalues, and abstract vector spaces, showing how they all fit together into a coherent mathematical framework. 

The stunning animations make abstract ideas feel concrete, allowing viewers to develop genuine intuition instead of relying on rote procedures. By emphasizing the why behind the mathematics, the playlist builds a strong conceptual foundation that benefits students, programmers, scientists, and anyone curious about how linear algebra describes the world. It is widely regarded as one of the best visual introductions to the subject and serves as an excellent companion to traditional textbooks and problem-solving practice. 


CALCULUS_PLAYLIST]]> by [3Blue1Brown]

Summary

The Essence of Linear Algebra playlist by 3Blue1Brown transforms what is often considered one of the most intimidating areas of mathematics into an intuitive and visually engaging experience. Rather than focusing on memorizing formulas or performing lengthy calculations, the series explains the geometric ideas behind vectors, matrices, and linear transformations, helping viewers understand what these concepts actually represent. As the lessons progress, it explores topics such as matrix multiplication, determinants, inverses, dot and cross products, changes of basis, eigenvectors, eigenvalues, and abstract vector spaces, showing how they all fit together into a coherent mathematical framework. 

The stunning animations make abstract ideas feel concrete, allowing viewers to develop genuine intuition instead of relying on rote procedures. By emphasizing the why behind the mathematics, the playlist builds a strong conceptual foundation that benefits students, programmers, scientists, and anyone curious about how linear algebra describes the world. It is widely regarded as one of the best visual introductions to the subject and serves as an excellent companion to traditional textbooks and problem-solving practice. 


CALCULUS_PLAYLIST]]> <![CDATA[Discrete Mathematics with Python [freecodecamp.org]]]> https://mklab.gr/showthread.php?tid=1110 Tue, 14 Jul 2026 17:56:07 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1110 [Image: 8ae84f6a-dfd2-4988-8f73-77e6f548846b.jpeg]
Discrete Mathematics with Python 
by [freecodecamp.org]

Summary

The course covers essential topics such as permutations, combinations, counting principles, set theory, prime numbers, modular arithmetic, graph-related ideas, and the Chinese Remainder Theorem, while also demonstrating many concepts with Python code. Instead of focusing only on formulas, it emphasizes understanding the reasoning behind mathematical ideas and how they are applied to algorithms, programming, and real-world problem solving. 

Created by former mathematics teacher and senior Python developer Karol Kurek, the beginner-friendly course gradually builds mathematical intuition through clear explanations and practical examples. By the end, learners gain a solid understanding of the core concepts that underpin software development, cryptography, data structures, and other areas of computing, making it an excellent starting point for anyone interested in mathematics or computer science.

COURSE PAGE



]]> [Image: 8ae84f6a-dfd2-4988-8f73-77e6f548846b.jpeg]
Discrete Mathematics with Python 
by [freecodecamp.org]

Summary

The course covers essential topics such as permutations, combinations, counting principles, set theory, prime numbers, modular arithmetic, graph-related ideas, and the Chinese Remainder Theorem, while also demonstrating many concepts with Python code. Instead of focusing only on formulas, it emphasizes understanding the reasoning behind mathematical ideas and how they are applied to algorithms, programming, and real-world problem solving. 

Created by former mathematics teacher and senior Python developer Karol Kurek, the beginner-friendly course gradually builds mathematical intuition through clear explanations and practical examples. By the end, learners gain a solid understanding of the core concepts that underpin software development, cryptography, data structures, and other areas of computing, making it an excellent starting point for anyone interested in mathematics or computer science.

COURSE PAGE



]]> <![CDATA[Lectures on Infinity [Hamkins]]]> https://mklab.gr/showthread.php?tid=1012 Fri, 10 Jul 2026 00:59:10 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1012 Lectures on Infinity 
BY [Joel David Hamkins]

Summary


Confronting the concept of infinity has challenged humanity's brightest minds for centuries, serving as a profound intersection where mathematics, philosophy, and theology meet. Historically framed by Aristotle’s crucial distinction between the potential infinite—an endless process of addition or division—and the actual infinite—a realized, completed whole—the study of the boundless has fundamentally reshaped our understanding of reality. This rich intellectual journey spans from the theological reflections of early scholars like St. Augustine to the mind-bending paradoxes that disrupted twentieth-century foundational logic.

David Hilbert’s famous Grand Hotel paradox brilliantly illustrates the counterintuitive nature of infinite sets, demonstrating how an establishment with infinitely many occupied rooms can still seamlessly accommodate new arrivals. Furthermore, Georg Cantor’s revolutionary work on transfinite numbers proved that not all infinities are created equal, revealing a breathtaking hierarchy of distinct sizes within the infinite realm itself. 

These deep mathematical inquiries culminate in Kurt Gödel’s incompleteness theorems, which exposed the inherent boundaries of formal systems. Ultimately, exploring these abstract landscapes does more than push the limits of logical reasoning; it fundamentally deepens our appreciation for the mysteries of human comprehension and permanently alters our relationship with the universe.

COURSE PAGE



]]> Lectures on Infinity 
BY [Joel David Hamkins]

Summary


Confronting the concept of infinity has challenged humanity's brightest minds for centuries, serving as a profound intersection where mathematics, philosophy, and theology meet. Historically framed by Aristotle’s crucial distinction between the potential infinite—an endless process of addition or division—and the actual infinite—a realized, completed whole—the study of the boundless has fundamentally reshaped our understanding of reality. This rich intellectual journey spans from the theological reflections of early scholars like St. Augustine to the mind-bending paradoxes that disrupted twentieth-century foundational logic.

David Hilbert’s famous Grand Hotel paradox brilliantly illustrates the counterintuitive nature of infinite sets, demonstrating how an establishment with infinitely many occupied rooms can still seamlessly accommodate new arrivals. Furthermore, Georg Cantor’s revolutionary work on transfinite numbers proved that not all infinities are created equal, revealing a breathtaking hierarchy of distinct sizes within the infinite realm itself. 

These deep mathematical inquiries culminate in Kurt Gödel’s incompleteness theorems, which exposed the inherent boundaries of formal systems. Ultimately, exploring these abstract landscapes does more than push the limits of logical reasoning; it fundamentally deepens our appreciation for the mysteries of human comprehension and permanently alters our relationship with the universe.

COURSE PAGE



]]> <![CDATA[Essence of Linear Algebra [3Blue1Brown ]]]> https://mklab.gr/showthread.php?tid=624 Mon, 22 Jun 2026 17:32:51 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=624 Essence of Linear Algebra
by  [ 3Blue1Brown ]

Summary

The playlist “Essence of Linear Algebra” by 3Blue1Brown is a visual introduction to the core ideas of linear algebra, focusing on intuition rather than only formulas. It explains vectors, linear combinations, span and basis, matrices as transformations, matrix multiplication, determinants, inverse matrices, vector spaces, dot products, cross products, change of basis, eigenvectors and eigenvalues, using animations to show the geometric meaning behind the concepts. The series aims to help learners understand why linear algebra works and why it is important in fields such as computer graphics, physics, data science, and machine learning. It contains 16 videos and is widely appreciated as a way to build a strong conceptual foundation before studying more formal linear algebra. 

PLAYLIST]]> Essence of Linear Algebra
by  [ 3Blue1Brown ]

Summary

The playlist “Essence of Linear Algebra” by 3Blue1Brown is a visual introduction to the core ideas of linear algebra, focusing on intuition rather than only formulas. It explains vectors, linear combinations, span and basis, matrices as transformations, matrix multiplication, determinants, inverse matrices, vector spaces, dot products, cross products, change of basis, eigenvectors and eigenvalues, using animations to show the geometric meaning behind the concepts. The series aims to help learners understand why linear algebra works and why it is important in fields such as computer graphics, physics, data science, and machine learning. It contains 16 videos and is widely appreciated as a way to build a strong conceptual foundation before studying more formal linear algebra. 

PLAYLIST]]> <![CDATA[Mathematical Modelling of Football]]> https://mklab.gr/showthread.php?tid=601 Mon, 22 Jun 2026 13:59:01 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=601 Mathematical Modelling of Football
BY UPSALA UNIVERSITY

Summary

This page outlines the syllabus for the Mathematical Modelling of Football course at Uppsala University, an open-source, project-based curriculum taught by David Sumpter that bridges academic mathematics with elite football analytics. Structured into three core blocks—Event Data, Tracking Data, and Advanced Applications—the course teaches students how to use Python to build statistical models, run simulations, map pitch control, and calculate advanced metrics like Expected Possession Value (EPV) using real-world data from providers like StatsBomb and Metrica. Developed in collaboration with top data scientists from clubs like Liverpool and Barcelona, the course requires a background in statistics and data science, featuring a workload of 10–15 hours per week structured around three major hand-in assignments.

COURSE]]> Mathematical Modelling of Football
BY UPSALA UNIVERSITY

Summary

This page outlines the syllabus for the Mathematical Modelling of Football course at Uppsala University, an open-source, project-based curriculum taught by David Sumpter that bridges academic mathematics with elite football analytics. Structured into three core blocks—Event Data, Tracking Data, and Advanced Applications—the course teaches students how to use Python to build statistical models, run simulations, map pitch control, and calculate advanced metrics like Expected Possession Value (EPV) using real-world data from providers like StatsBomb and Metrica. Developed in collaboration with top data scientists from clubs like Liverpool and Barcelona, the course requires a background in statistics and data science, featuring a workload of 10–15 hours per week structured around three major hand-in assignments.

COURSE]]> <![CDATA[18.06 Linear Algebra [MIT]]]> https://mklab.gr/showthread.php?tid=496 Thu, 18 Jun 2026 23:39:28 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=496 Summary

MIT OpenCourseWare’s 18.06 Linear Algebra (Spring 2010) is a free undergraduate course taught by Prof. Gilbert Strang that introduces the fundamental ideas of matrix theory and linear algebra. The course covers systems of equations, vector spaces, subspaces, determinants, eigenvalues, eigenvectors, diagonalization, similarity, orthogonality, least squares, positive definite matrices, and applications such as graphs, networks, differential equations, Fourier methods, and linear programming.

 It provides video lectures, lecture notes, problem sets with solutions, exams, and other study materials, making it one of the most popular self-study resources for learning linear algebra with a balance of theory, computation, and real-world applications. 

COURSE]]> Summary

MIT OpenCourseWare’s 18.06 Linear Algebra (Spring 2010) is a free undergraduate course taught by Prof. Gilbert Strang that introduces the fundamental ideas of matrix theory and linear algebra. The course covers systems of equations, vector spaces, subspaces, determinants, eigenvalues, eigenvectors, diagonalization, similarity, orthogonality, least squares, positive definite matrices, and applications such as graphs, networks, differential equations, Fourier methods, and linear programming.

 It provides video lectures, lecture notes, problem sets with solutions, exams, and other study materials, making it one of the most popular self-study resources for learning linear algebra with a balance of theory, computation, and real-world applications. 

COURSE]]> <![CDATA[ECE 204 Numerical methods]]> https://mklab.gr/showthread.php?tid=316 Sat, 13 Jun 2026 13:04:05 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=316
ECE 204: Numerical Methods at the University of Waterloo is an engineering course focused on designing and applying algorithms to approximate solutions to mathematical problems where exact calculations are impossible due to the limitations of computer floating-point representations. The curriculum is structured around seven foundational tools—weighted averages, iteration, linear algebra, interpolation, Taylor series, bracketing, and the intermediate-value theorem—which students use to solve problems across four distinct categories: signal approximation (derivatives and integrals of discrete, often noisy data), solving single and systems of equations, analyzing ordinary and partial differential equations (like heat and wave equations), and executing unconstrained optimization. Unlike traditional numerical methods courses, it uniquely emphasizes real-time system constraints, fixed sampling rates, and handling noisy sensor data using least-squares approximations rather than standard textbook extrapolations.

COURSE PAGE]]>
ECE 204: Numerical Methods at the University of Waterloo is an engineering course focused on designing and applying algorithms to approximate solutions to mathematical problems where exact calculations are impossible due to the limitations of computer floating-point representations. The curriculum is structured around seven foundational tools—weighted averages, iteration, linear algebra, interpolation, Taylor series, bracketing, and the intermediate-value theorem—which students use to solve problems across four distinct categories: signal approximation (derivatives and integrals of discrete, often noisy data), solving single and systems of equations, analyzing ordinary and partial differential equations (like heat and wave equations), and executing unconstrained optimization. Unlike traditional numerical methods courses, it uniquely emphasizes real-time system constraints, fixed sampling rates, and handling noisy sensor data using least-squares approximations rather than standard textbook extrapolations.

COURSE PAGE]]> <![CDATA[Probabilistic Systems Analysis and Applied Probability [MIT]]]> https://mklab.gr/showthread.php?tid=293 Thu, 11 Jun 2026 20:32:01 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=293 Probabilistic Systems Analysis and Applied Probability
Summary 
MIT 6.041 / 6.431: Probabilistic Systems Analysis and Applied Probability (Fall 2010), taught by Professor John Tsitsiklis, is a foundational undergraduate/graduate course designed to introduce the concepts, mathematical frameworks, and tools used to model and analyze random phenomena and engineering systems under uncertainty.
The course emphasizes building a strong conceptual understanding and probabilistic intuition alongside strict mathematical derivations.
COURSE PAGE
]]> Probabilistic Systems Analysis and Applied Probability
Summary 
MIT 6.041 / 6.431: Probabilistic Systems Analysis and Applied Probability (Fall 2010), taught by Professor John Tsitsiklis, is a foundational undergraduate/graduate course designed to introduce the concepts, mathematical frameworks, and tools used to model and analyze random phenomena and engineering systems under uncertainty.
The course emphasizes building a strong conceptual understanding and probabilistic intuition alongside strict mathematical derivations.
COURSE PAGE
]]> <![CDATA[CS103: Mathematical Foundations of Computing]]> https://mklab.gr/showthread.php?tid=288 Thu, 11 Jun 2026 19:03:19 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=288 CS103: Mathematical Foundations of Computing
Summary
CS103: Mathematical Foundations of Computing at Stanford is a core course exploring the limits of what computers can solve, how they do it, and why some problems are harder than others. It trades calculus for discrete mathematics, logic, and theoretical models.
The course is divided into four main areas:

  1. Mathematical Logic & Proofs: Covers sets, formal proof techniques (contradiction, induction), first-order logic, functions, and graph theory to build mathematical rigor.
  2. Automata Theory: Explores simple mathematical models of computation, including Finite Automata (DFAs/NFAs), Regular Expressions, and Context-Free Grammars.
  3. Computability Theory: Introduces Turing Machines to define the absolute limits of computing, culminating in proofs of unsolvable problems like the Halting Problem.
  4. Complexity Theory: Examines efficiency, focusing on the famous P vs. NP question and how to classify problems that are computationally difficult (NP-Completeness).
COURSE PAGE
]]> CS103: Mathematical Foundations of Computing
Summary
CS103: Mathematical Foundations of Computing at Stanford is a core course exploring the limits of what computers can solve, how they do it, and why some problems are harder than others. It trades calculus for discrete mathematics, logic, and theoretical models.
The course is divided into four main areas:

  1. Mathematical Logic & Proofs: Covers sets, formal proof techniques (contradiction, induction), first-order logic, functions, and graph theory to build mathematical rigor.
  2. Automata Theory: Explores simple mathematical models of computation, including Finite Automata (DFAs/NFAs), Regular Expressions, and Context-Free Grammars.
  3. Computability Theory: Introduces Turing Machines to define the absolute limits of computing, culminating in proofs of unsolvable problems like the Halting Problem.
  4. Complexity Theory: Examines efficiency, focusing on the famous P vs. NP question and how to classify problems that are computationally difficult (NP-Completeness).
COURSE PAGE
]]> <![CDATA[6.1200J Mathematics for Computer Science [MIT]]]> https://mklab.gr/showthread.php?tid=180 Tue, 09 Jun 2026 03:23:02 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=180 Mathematics for Computer Science
This course covers elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability
COURSE PAGE
LECTURES
]]> Mathematics for Computer Science
This course covers elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability
COURSE PAGE
LECTURES
]]> <![CDATA[Measure Theory (2018) [Claudio Landim]]]> https://mklab.gr/showthread.php?tid=46 Sun, 30 Mar 2025 14:02:41 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=46
===> https://www.youtube.com/playlist?list=PL...QHej3F6RFX]]>
===> https://www.youtube.com/playlist?list=PL...QHej3F6RFX]]> <![CDATA[Introduction to number theory [Borcherds]]]> https://mklab.gr/showthread.php?tid=44 Fri, 28 Mar 2025 10:50:14 +0200 mklabgr]]> https://mklab.gr/showthread.php?tid=44
https://www.youtube.com/playlist?list=PL...AOpuZ1Fov8]]>
https://www.youtube.com/playlist?list=PL...AOpuZ1Fov8]]> <![CDATA[Learn Linear Algebra for Machine Learning [freecodecamp.org]]]> https://mklab.gr/showthread.php?tid=32 Sun, 16 Mar 2025 16:23:06 +0200 mklabgr]]> https://mklab.gr/showthread.php?tid=32
https://www.youtube.com/watch?v=QCPJ0VdpM00]]>
https://www.youtube.com/watch?v=QCPJ0VdpM00]]>