Pure Mathematics Courses and Certifications

Cryptography I

53 ratings

Cryptography is an indispensable tool for protecting information in computer systems. In this course you will learn the inner workings of cryptographic systems and how to correctly use them in real-world applications.

• Coursera
• 23 hours
• Self-Paced
• Paid Course

• Best of All Time

Insights into Mathematics

Sociology and Pure Mathematics - Pure Mathematics Relies on a Fake Arithmetic

Challenges modern pure mathematics' reliance on "fake arithmetic," proposing alternative approaches to calculus without infinite processes and calling for sociological analysis of mathematical practices.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Big Mathematics Divide - Between "Exact" and "Approximate" - Sociology and Pure Maths

Explores the divide between exact and approximate theories in pure mathematics, challenging conventional views on arithmetic, algebra, topology, and number theory, including the Riemann Hypothesis.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Is Pure Mathematics Logically Viable? Five Challenges - Sociology and Pure Maths

Exploring five challenges to pure mathematics' logical viability, this talk critically examines the field's foundations and encourages reevaluation of its core principles and practices.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Emile Borel - Real Number Enthusiast or Skeptic? - Sociology and Pure Mathematics

Explore Emile Borel's contributions to measure theory and his skepticism about real numbers, including normal numbers and the intriguing concept of a "know-it-all" number.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Euclid Book 1 Props I - V - A Critical Review - Sociology and Pure Mathematics - N J Wildberger

Critical review of Euclid's Book 1 Propositions I-V, examining logical foundations and constructions. Explores historical significance and questions modern interpretations of Euclidean geometry.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Insights into Mathematics

John Keil's Preface to Euclid - Sociology and Pure Mathematics

Exploration of John Keil's 1723 preface to Euclid's Elements, discussing its historical context and significance in geometry, including comparisons to Isaac Barrow's version.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Emperor's Functions Have No Clothes - Sociology and Pure Mathematics

Uncover the logical flaws in modern set-theoretic function definitions and explore alternative approaches to this fundamental mathematical concept.

• YouTube
• 12 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Definitional Weaknesses of Pure Mathematics Courses - Sociology and Pure Mathematics

Uncover critical logical flaws in pure mathematics education, examining definitional weaknesses in fundamental concepts like numbers, functions, and sequences.

• YouTube
• 16 minutes
• Self-Paced
• Free Video

Michael Penn

What Mathematicians Mean When We Use Super as a Prefix

Explore the mathematical meaning of "super" as a prefix, delving into its applications and significance in various mathematical contexts.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Michael Penn

What Is It Like to Be a Pure Mathematician?

Explore the life of a pure mathematician, delving into abstract algebra, group theory, and partitions. Gain insights into the field's challenges, problem-solving approaches, and the beauty of elegant proofs.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The One Dimensional Random Walk Hypergroup - Diffusion Symmetry

Explore affine transformations, representation theory, and random walks on a 1D lattice. Learn about hypergroups and calculate probabilities in this advanced mathematics lecture.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Particle Collisions, Hypergroups and Quadratic Residues - Diffusion Symmetry 3

Explore particle collision models, hypergroups, and quadratic residues in algebraic structures. Learn about fusion rule algebras, complete graphs, and primitive roots in prime fields.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The S3 Character Table - A New Meaning - Diffusion Symmetry

Explore the S3 character table from a diffusion symmetry perspective, uncovering new interpretations in group theory, combinatorics, and algebraic structures.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Translating Polynumbers and the Derivative - Arithmetic and Geometry Math Foundations

Explore polynomials and derivatives algebraically, introducing Taylor polynomials and sub-derivatives. Challenges traditional calculus views, shifting towards Euler and Lagrange's approach to mathematical foundations.

• YouTube
• 37 minutes
• Self-Paced
• Free Video