Red-Green-Code

Deliberate practice techniques for software developers

  • Home
  • About
  • Contact
  • Project 462
  • CP FAQ
  • Newsletter

Archives for February 2019

How to Practice Writing Proofs

By Duncan Smith Leave a Comment Feb 27 0

Proof

Proof-writing skills are important for all college-level math. But there’s a special relationship between proofs and discrete math. In the “Goals of a Discrete Mathematics Course” section in the preface to his textbook, Rosen puts Mathematical Reasoning first in the list. He writes:

Students must understand mathematical reasoning in order to read, comprehend, and construct mathematical arguments [proofs]. This text starts with a discussion of mathematical logic, which serves as the foundation for the subsequent discussions of methods of proof. Both the science and the art of constructing proofs are addressed.

Rosen Chapter 1 is “The Foundations: Logic and Proofs,” and that chapter ends with sections on “Introduction to Proofs” and “Proof Methods and Strategy.” A textbook that specifically covers proof techniques, Daniel J. Velleman’s How to Prove It, begins with chapters on these same topics, and includes chapters on logic and on mathematical induction which Rosen also covers. So it’s not surprising that many of the exercises in Rosen ask for proofs. Here is a process I use to get the most out of these exercises.

« Continue »

How to Read a Math Textbook

By Duncan Smith Leave a Comment Feb 22 0

Textbook

If you search for advice on how to read a math textbook, you’ll find plenty to choose from. I’ll link to some of my favorites at the end of this article. But first, here’s an overview of my experience reading math books, and what techniques I found to be useful.

« Continue »

What is Discrete Mathematics?

By Duncan Smith Leave a Comment Feb 16 0

Discrete math books

In their first 13 or so years of school, students cover a standardized math curriculum. Last week, I covered how Khan Academy approaches that curriculum. Notably absent from that list are many topics in discrete mathematics. But what is discrete mathematics, anyway? I’ll answer that in two ways: with a definition, and with a curriculum.

« Continue »

The Khan Academy Math Course System

By Duncan Smith Leave a Comment Feb 7 0

Calculus

Khan Academy’s math program is designed to help children and young adults learn and practice a particular set of math skills. These skills map to school curricula like the US Common Core, so that when students learn something on the site, it translates to success in the classroom. But Khan Academy can also help adults review the fundamental skills necessary to learn more advanced math. The idea is to fill in “swiss cheese gaps” in knowledge that often accumulate when learning math in school. These gaps can slow down further learning, since math success in later courses depends on knowing the skills taught in previous courses.

This week, I’ll go over the topics available on Khan Academy. Next week, I’ll look at how they relate to discrete math topics.

« Continue »

Stay in the Know

I'm trying out the latest learning techniques on software development concepts, and writing about what works best. Sound interesting? Subscribe to my free newsletter to keep up to date. Learn More
Unsubscribing is easy, and I'll keep your email address private.

Getting Started

Are you new here? Check out my review posts for a tour of the archives:

  • • 2015 Summer Review
  • • 2015 in Review
  • • 2016 in Review
  • • What I Learned Working On Time Tortoise in 2017
  • • Competitive Programming Frequently Asked Questions: 2018 In Review

Archives

  • December 2019 (2)
  • November 2019 (4)
  • October 2019 (5)
  • September 2019 (4)
  • August 2019 (4)
  • July 2019 (5)
  • June 2019 (4)
  • May 2019 (5)
  • April 2019 (4)
  • March 2019 (4)
  • February 2019 (4)
  • January 2019 (5)
  • December 2018 (4)
  • November 2018 (4)
  • October 2018 (5)
  • September 2018 (4)
  • August 2018 (5)
  • July 2018 (4)
  • June 2018 (4)
  • May 2018 (5)
  • April 2018 (4)
  • March 2018 (4)
  • February 2018 (4)
  • January 2018 (5)
  • December 2017 (4)
  • November 2017 (5)
  • October 2017 (4)
  • September 2017 (4)
  • August 2017 (5)
  • July 2017 (4)
  • June 2017 (4)
  • May 2017 (5)
  • April 2017 (4)
  • March 2017 (5)
  • February 2017 (4)
  • January 2017 (4)
  • December 2016 (4)
  • November 2016 (5)
  • October 2016 (4)
  • September 2016 (4)
  • August 2016 (5)
  • July 2016 (4)
  • June 2016 (5)
  • May 2016 (4)
  • April 2016 (4)
  • March 2016 (5)
  • February 2016 (4)
  • January 2016 (4)
  • December 2015 (5)
  • November 2015 (4)
  • October 2015 (4)
  • September 2015 (5)
  • August 2015 (4)
  • July 2015 (5)
  • June 2015 (4)
  • May 2015 (4)
  • April 2015 (5)
  • March 2015 (4)
  • February 2015 (4)
  • January 2015 (4)

Recent Posts

  • Quora Experiment 2019: Week 24
  • Quora Experiment 2019: Week 23
  • Quora Experiment 2019: Week 22
  • Quora Experiment 2019: Week 21
  • Quora Experiment 2019: Week 20
Red-Green-Code
  • Home
  • About
  • Contact
  • Project 462
  • CP FAQ
  • Newsletter
Copyright © 2019 Duncan Smith