Zach Haney
  • Member for 7 years, 9 months
  • Last seen more than 3 years ago
  • Boston, MA, USA
What can be said about Lie groups in a first abstract algebra course?
11 votes

I suggest having a look at the following book by John Stillwell: Naive Lie Theory. A fast-paced week or (if you're lucky enough... or believe it's worth it as I would) two weeks could be created by ...

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How to teach calculus (book recommendation)
7 votes

There are so many Calc 1, 2, and Multi video lectures online now. Watch a few... take notes on what you think are some good traits of the person teaching. MIT's Calc course (super fast) might be ...

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How and when should I introduce my students to WolframAlpha?
6 votes

[Long winded response!] Although I do enjoy Sage, I have to agree with others that it is not quite user-friendly enough for high schoolers to tolerate just yet. I would also echo those that discount ...

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Why is the convergence of infinite series covered in Calculus II?
5 votes

One could make a lot of arguments either way. However, with respect to the AP curriculum as it stands, it makes sense to include infinite series, because Taylor Series are there. Why do I say this? ...

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Solving a Polar set of equations algebraically?
4 votes

What about taking what @whatever got: $ (4\cos^2(\theta)-1)^2(1-\cos^2(\theta)) \cos^2(\theta)=1$. Let $ x = \cos(\theta).$ This gives us a more familiar looking: $(4x^2-1)^2(1-x^2)x^2=1$, which we ...

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Teaching the History of Mathematics in High School
4 votes

In teaching a course on geometry to sophomore's in the previous year, I definitely included as much history as possible. There are numerous ways to do this. The first thing is that -- like @Cameron ...

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Graphing functions from a finite field to itself
4 votes

Perhaps an approach that mirrors the standard graphing might be useful? One way that I appreciate is seen here: This is used by N. J. Wildberger and others. I just snagged this off google images to ...

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Worksheet: Homology in Intro Lin Al
3 votes

I am a huge fan of using tools in a current math course to show something "flashy" or more advanced. It's especially nice if you can really ham it up and make people think they're doing something that ...

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Geometry with a view towards differential geometry textbook
3 votes

You might consider basing your course on the Differential Geometry lectures given by Dr. N. J. Wildberger [found on youtube, link below.] He has some idiosyncrasies that you can clearly ignore, but ...

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A companion on the Journey Through Genius
3 votes

John Stillwell's "Mathematics and its History" -- exercises and all. I have used Stillwell's book to connect with the readings in Journey Through Genius, so it is worth looking at for more context ...

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A basic game to make arguments about
3 votes

You might also consider the game Set. https://en.wikipedia.org/wiki/Set_(game) shows some of the basic games with the cards and some associated combinatorics. I also have some more materials for this ...

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Devising backup plan to become HS teacher as a late undergrad
3 votes

On the website for schools in NY state (if you're hoping to stay there), there are many options suggested for alternate routes to certification that you may be able to pursue. However, these do have ...

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Should my 8th graders see a proof of the Pythagorean Theorem?
2 votes

A broader answer regarding the teaching of the Pythagorean Theorem (including the proof): http://www.magicalmaths.org/could-this-be-the-best-pythagoras-theorem-lesson-ever/ And an image from the ...

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Why do we teach complex numbers?
2 votes

I highly suggest you obtain a (used) copy of the CME Project Algebra 2 (orange) textbook and look at its section on complex numbers. They should be thought of as very geometric objects - they apply to ...

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What makes cosets hard to understand?
2 votes

Jessica, Norman Wildberger has a few interesting approaches to thinking about quotient groups, leading up to him talking about homology in his intro Algebraic Topology course. I cannot remember which ...

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Extensions beyond Euclidian Geometry for Secondary students
2 votes

Taxicab Geometry!! Show your students how to pose problems in mathematics. Get them posing their own geometric questions. What if I change that definition/axiom, for example? For example: http://...

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Honors project idea for linear algebra
2 votes

James, If you have the book, you could have your student read in David Poole's Linear Algebra, chapter 2.4, there is a section on Finite Linear Games as related to systems of equations. There is also ...

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How should I teach linear algebra and vector geometry together at high school?
Accepted answer
2 votes

The CME project is working very hard to make this happen more in high schools. Although they haven't published their book yet (coming this winter!), they have an outline of the material on this ...

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What is a free and simple 3D plot software for students?
2 votes

A new player on the scene is called Desmos. It's oddly... pretty. It's also super simple to use. The website is here: Desmos Sliders can be added rather easily. If you're in the calculator and want ...

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Textbook for first course in linear algebra
1 votes

I would back up @Alexander-Woo for Poole's text as well as offer the suggestion for Shifrin's "Linear Algebra - A Geometric Approach". None of these books are really affordable. There was a ...

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Pedagogical quandary with the definition of $i$
1 votes

Celeriko, I'll directly respond to your exact question first then rant on about my real feelings after :) You are exactly right that this alleged definition which your standards is using is to say ...

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