Logical Foundations of Mathematics

Study sheet

This topic examines the axiomatic foundations and logical systems that underpin mathematical reasoning. You will understand the historical development of set theory, proof theory, and model theory, and how they address questions of mathematical truth and consistency.

11 resources

Level

Language

Type

📹Videos(1)

video👁️ 0

Mathematical Logic Playlist

Introductory series on logic foundations from Reddit recs

beginner🇬🇧

🎓Courses(4)

course👁️ 0

Mathematical Logic

Learn mathematical logic with Hans-Peter Beck! Explore the logical foundations of mathematics in this comprehensive course.

advanced🇬🇧

course👁️ 0

Automata, Computability, and Complexity

Explore automata, computability, and complexity with Michael Sipser's comprehensive course. Master the theory of computation!

advanced🇬🇧

course👁️ 0

Logic for Computer Science

Unlock the power of logical thinking and formal reasoning essential for success in computer science, data analysis, and software development with this dynamic course. Ideal for students, software engineers, data scientists, and IT professionals, this comprehensive program delves into logic foundations critical for advanced computing careers. Starting with fundamental proofs and proof systems, you’ll explore soundness, completeness, first-order propositional, and predicate logic. Dive into advanced topics like modeling, program verification, and temporal logic. Master Gentzen’s natural deduction, and understand the semantics and syntax of logical forms. Tackle the undecidability of logic and learn model checking using temporal logics (LTL, CTL, CTL*) to verify system properties, applying Floyd-Hoare logics to ensure program correctness. Our structured approach incorporates practical techniques to enhance memory and overcome procrastination, benefiting both academic learning and professional efficiency. Engaging case studies offer hands-on experience verifying algorithms, such as array searching and sorting, essential for real-world problem solving. Geared towards those aiming for roles in tech innovation, this course equips you with the analytical tools and logical proficiency to excel in computing, programming, and data-driven problem-solving. Elevate your career and expertise in the ever-evolving technology landscape.

beginner🇬🇧

course👁️ 2

Introduction to Mathematical Thinking

Learn how to think the way mathematicians do – a powerful cognitive process developed over thousands of years. Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.

beginner🇬🇧

📚Books(2)

book👁️ 0

How to Prove It - Daniel J. Velleman

A clear, step-by-step transition from computational math to proof-based math, focusing on logic and set theory.

beginner🇬🇧

book👁️ 0

Foundations of Mathematics

Foundations of Mathematics - A book resource

intermediate🇬🇧

🌐Websites(4)

website👁️ 0

nLab: Foundations of Mathematics

Modern perspectives including HoTT

beginner🇬🇧

website👁️ 0

mathworld.wolfram.com

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

intermediate🇬🇧

website👁️ 0

ocw.mit.edu

MIT OpenCourseWare is a free, publicly accessible repository of MIT course materials across many disciplines, providing complete lecture notes, assignments, exams, and often video lectures from MIT courses. It includes math and other subjects, allowing self-paced study on topics such as group theory and beyond.

intermediate🇬🇧

website👁️ 0

plato.stanford.edu

The Stanford Encyclopedia of Philosophy is a peer‑reviewed online encyclopedia of philosophy featuring in‑depth, scholarly articles written and regularly updated by experts, including comprehensive coverage of logic topics.

intermediate🇬🇧

Frequently Asked Questions

What are the best free resources to learn Logical Foundations of Mathematics?

Dantes has curated 11 resources for Logical Foundations of Mathematics, including 1 videos, 2 books, 4 courses, 4 websites. All resources are hand-picked for quality — no algorithmic filler. Browse the full list above to find the format that works best for you.

Is Logical Foundations of Mathematics hard to learn?

Logical Foundations of Mathematics is approachable at the beginner level — there are resources here specifically for those starting from scratch. As you progress, intermediate and advanced material is also available to take your skills further.

What types of Logical Foundations of Mathematics learning resources are available on Dantes?

For Logical Foundations of Mathematics, Dantes has curated 1 videos, 2 books, 4 courses, 4 websites. Each resource type serves a different learning style: videos and YouTube for visual learners, books for depth, courses for structured progression, and websites for quick reference.

How does Dantes select Logical Foundations of Mathematics resources?

Dantes is an algorithm-free learning directory. Resources are hand-curated based on quality, accuracy, and usefulness — not engagement metrics or paid placements. The goal is to surface the best learning material for Logical Foundations of Mathematics, whether it's a free YouTube series, a classic textbook, or an open courseware from a top university.

Go deeper

Test your understanding of Logical Foundations of Mathematics

Explain it out loud. An AI tutor listens and asks questions that expose gaps you didn't know you had.