The notes cover introduction to proofs, axioms of fields, complex numbers, some topology, and limits, continuity, derivatives, integrals, sequences and series. For teaching proof writing, many proofs contain in red color parts of proofs that should not be written down but should be thought.
Mathematics as a Non-Superstition. Eleven math courses (in the playlists), from high school (precalculus) to early graduate school (functional analysis), taught in such a way that the student should be able to defend (almost) all statements against objection.
Playlist List (sorted by last added):
Course 4: Linear Algebra
Course 3: Calculus II (US)
Course 2: Calculus I (Another extra)
Course 7: Principles of Mathematical Analysis
Course 9: Basic Functional and Harmonic Analysis
Course 8: Fourier Analysis
Course 8: Complex Analysis
Course 6: Introduction to Analysis
Course 5: Differential Equations
Course 4: Multivariable Calculus
Course 3: Calculus II
Course 2: Calculus I
Course 1: Precalculus
Principles of Mathematical Analysis (based on Rudin's book of that name, Chapters 1, 2, 4, 5, 3, 7). (Prerequisites: some familiarity with theoretical mathem...
An introduction to theoretical mathematics via the basic concepts of analysis: fields, the real numbers, least upper bounds, the limit, sequences, Cauchy seq...
M. Lochau, S. Mennicke, H. Baller, and L. Ribbeck. Leveraging Applications of Formal Methods, Verification and Validation. Technologies for Mastering Change, volume 8802 of Lecture Notes in Computer Science, Springer Berlin Heidelberg, (2014)