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
V. Mazurov, и E. Khukhro. (2014)cite arxiv:1401.0300Comment: A few new solutions and references have been added. Preparation of the next 19th issue is underway, new problems are welcome, as well as comments on previous editions.
P. Nagy, P. Surján, и Á. Szabados. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), 131 (2):
1-6(февраля 2012)
G. Davis, и M. Mcgowen. proceedings of the Annual Meeting of the 26th Annual Meeting of the International Group for the Psychology of Mathematics Education (PME), 2, стр. 273-280. Norwich, UK, University of Norwich, (июля 2002)
C. Bergsten. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, 2, стр. 153-160. Prague, Czech Republic July 16-21, (2006)
L. Lee. Approaches to algebra: perspectives for research and teaching, Kluwer Academic Publishers, p 102
… it is much of a challenge to demonstrate that functions, modelling, and problem solving are all types of generalizing activities, that algebra and indeed all of mathematics is about generalizing patterns.
p 103
The history of the science of algebra is the story of the growth of a technique for representing of finite patterns.
The notion of the importance of pattern is as old as civilization. Every art is founded on the study of patterns.
Mathematics is the most powerful technique for the understanding of pattern, and for the analysis of the relationships of patterns.(1996)
D. Carraher, A. Schliemann, и B. Brizuela. Proceedings of the XXV Conference of the International Group for the Psychology of Mathematics Education, (2001)
J. Houssart, и H. Evens. Proceedings of the sixth British Congress of Mathematics Education held at the University of Warwick, стр. 65-72. bsrlm, (2005)
L. Saldanha, и P. Thompson. Proceedings of the Annual Meeting of the Psychology of Mathematics Education - North America, Raleigh, NC, North Carolina State University, (1998)