Keith Devlin Coursera Introduction to Mathematical Thinking goes live

I have signed up and indicated I am a tutor.  I am in the Alexandria, VA area.

Looks interesting.  Devlin has taken this course very seriously.

Angry Math criticizes another course, not given by Devlin.

10 percent finish. Even though you can retry in at least some courses for the homework and/or exam.

Plagiarism in the courses.

The process of taking a quiz can help.  So some people get some value.

MOOCs as structured now are just play.


Let me not forget to plug my own books as a way to learn mathematical induction.  The Lance Rips Asmuth et al research shows that students find the hardest block to learning mathematical induction is quadratic or higher algebra in the formulas.

My books in Peano Axioms have no such formulas but still have many proofs in mathematical induction.  This is because they work on relationships among natural numbers such as the associative and commutative laws of addition.


Math thinking is not defined by Devlin?
But Lance Rips and Jennifer Asmuth have a paper that we might say studies math thinking in students.

One hypothesis we might formulate from the Lance Rips and Asmuth paper above is that students find complicated algebra formulas so daunting they can’t see the mathematical induction principle.


Following paper is very valuable to discuss what is mathematical thinking.



=On my two volumes so far on Peano Arithmetic.

Entire book Geometry of Addition is approximately 240 pages of material when formatted as a pdf. The entire book contains a total of 270 exercises, 119 lemmas, 30 note fields, 6 web url note fields, 161 examples, and 54 definitions. This is a total of 640 fields. This is in addition to the text. It is organized into 33 chapters. Fields and chapters are renumbered within each part of the overall work.

The first volume Peano Axioms has 178 Examples, 463 Exercises, 98 definitions, 45 Lemmas with proofs, references to over 96 web pages, 58 chapters, and is 391 pages when formatted as pdf with Latex. 178 examples + 463 exercises + 98 definitions + 45 lemmas + 96 webpages equals 880. Added to the 640 fields above is 1520 fields. This is in addition to the text not in such fields.

Total examples is 178 + 161 = 339 examples. 463 + 270 = 733 Exercises. 54 + 98 = 152 definitions. 119+45 = 164 lemmas. 96+6 = 102 web page references. 58+33 = 91 chapters. 391 + 240 = 631 pages.

There are no quadratic or higher algebra formulas. Students complain about complicated algebra in learning how to do proofs by mathematical induction. This material is thus the ideal for learning mathematical induction proofs.


Author page with books to purchase.

Not all of Geometry of Addition is posted yet as of this Saturday morning.

Students taking Devlin’s Introduction to Mathematical Thinking at Coursera or the other Cousera course on logic starting in September 2012, will find my e-books very useful to get easy to do problems to get started instead of hard problems right away.


About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
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