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:

  • Lessons from the 2020 LeetCode Monthly Challenges
  • 2019 in Review
  • Competitive Programming Frequently Asked Questions: 2018 In Review
  • What I Learned Working On Time Tortoise in 2017
  • 2016 in Review
  • 2015 in Review
  • 2015 Summer Review

Archives

Recent Posts

  • LeetCode 1022: Sum of Root To Leaf Binary Numbers January 27, 2021
  • LeetCode 1288: Remove Covered Intervals January 20, 2021
  • LeetCode 227: Basic Calculator II January 13, 2021
  • A Project for 2021 January 6, 2021
  • Lessons from the 2020 LeetCode Monthly Challenges December 30, 2020
  • Quora: Are Math Courses Useful for Competitive Programming? December 23, 2020
  • Quora: Are Take-Home Assignments a Good Interview Technique? December 17, 2020
  • Quora: Why Don’t Coding Interviews Test Job Skills? December 9, 2020
  • Quora: How Much Time Should it Take to Solve a LeetCode Hard Problem? December 2, 2020
  • Quora: Quantity vs. Quality on LeetCode November 25, 2020
Red-Green-Code
  • Home
  • About
  • Contact
  • Project 462
  • CP FAQ
  • Newsletter
Copyright © 2021 Duncan Smith