Greg Stanton

@HigherMathNotes

Professional math tutor. Uploading my math education to YouTube, one video at a time.

Vrijeme pridruživanja: lipanj 2016.

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  1. Prikvačeni tweet
    8. lip 2016.

    "What is a differential equation?" First video in my growing diff eq playlist!

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  2. proslijedio/la je Tweet
    31. sij

    We are partnering with AFIT in Dayton, Ohio to support 1-2 paid summer fellowship positions for teachers to create classroom activities that mix CS, science and mathematics concepts! Key goal is to broaden the "pipeline" of students who receive CS training

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  3. 25. sij

    One of my Calc 3 students is taking an accredited online course that uses free YouTube videos. But, the $168 textbook is a barrier. Let's spread the word to instructors: it's not just video... there are textbooks too! Just ask or !

    Tutoring notes 
Derivation of 3D distance formula

A box is shown, with coordinates given for opposite corners, connected by a diagonal of length d, which is the hypotenuse of a right triangle whose legs are a diagonal of the base and a vertical box edge.

The diagonal of the base is the hypotenuse of another right triangle (its legs are base edges).

Two applications of the Pythagorean theorem finish the derivation.
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  4. 16. sij

    I'm definitely keeping this resource in mind for my multivariable students this semester. : Check out the updated course trailer for a glimpse of Prof G's innovative curriculum and boundless creativity!

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  5. 10. sij

    Retweeting this so I remember to check out this blog before the next time I visit my nieces and nephews! Sounds like a great resource. Now I'm wondering if any of the activities I came up with and tweeted about were already on 's blog...

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  6. 10. sij

    If you're interested in interactive textbooks, or in visualizing complex analysis, check out this new online book by , built with free technologies like and !

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  7. 10. sij

    WHY are the slopes of perpendicular lines opposite reciprocals? Here's an elementary, literal back-of-the-envelope proof. Coincidentally, I've found a new application of : it's a great way to reuse all of that vexing !

    A proof that perpendicular lines have opposite reciprocal slopes.

Two perpendicular lines are shown. In one of the quadrants they delineate, two adjacent right triangles are drawn, each giving the slope of one of the lines (via a ratio of sides).

One triangle has legs measuring 1 and m. The other triangle is similar, obtained from the first by a scale factor of 1 / m. Orientation produces the opposite sign.
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  8. 23. pro 2019.

    Currently, journal articles based on federally funded research must be made free w/in 12 months of publication. A new proposal would eliminate the wait; some publishers & academic societies are opposing this . Thankfully, and are not in this group!

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  9. 23. pro 2019.

    Kids can have fun trying out different strategies, which can lead them to discover search algorithms! Linear search is a simple one; binary search is depicted in the first tweet.

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  10. 23. pro 2019.

    2/Rules: All agree on a whole number n for each round, e.g. n = 100, and a player to be the arbiter, e.g. P1. 1. P1 chooses a number m from 0, 1, ..., n and keeps it secret. 2. P2 guesses until determining m. Optionally, winner can be the player requiring the fewest guesses.

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  11. 23. pro 2019.

    1/Yesterday, my niece discovered a known algorithm while playing a game I made up on a family trip called "Guess My Number." She remembered the game over a year later and spontaneously asked to play it! I'll share the super simple rules in this thread.

    An array is shown as a row of adjoining boxes, indexed from zero to eleven. The entries in the boxes are labeled A_0, A_1, ... , A_11, except for the entry at index 7, which is labeled as T (which stands for target).

Above the array is a sequence of vertical arrows pointing to boxes indexed by 5, 8, 6, and 7, in that order. 

This depicts binary search.
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  12. 19. pro 2019.

    : Do you cover probability in class? It motivates improper integrals / infinite series, meshes with physical applications (probability is analogous to mass), and supports science and statistics! In the curriculum, maybe it could "displace" fluid force?

    A drawing of the exponential distribution, showing a graph of the probability density function, with the area underneath the curve shaded from zero up to a positive value on the x-axis, which corresponds to the cumulative distribution function at that value. 

Formulas are shown on the side:

f_x(x) = lambda*e^(-lambda*x)
F_x(x) = 1 - e^(-lambda*x)
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  13. 16. pro 2019.

    Here's the code for computing Φ using Taylor series: Again, all the values I tested match the entries in standard reference tables. Very satisfying!

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  14. 16. pro 2019.

    Here's the code for computing Φ using Simpson's rule: There's not much code. It's mostly comments (including an explanation of the mathematics used to bound the error). It works pretty well! The values seem to match standard reference tables exactly.

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  15. 16. pro 2019.

    You can try the interactive app and see my for it, hosted . (Their Intro to JS course, led by , does a great job teaching the coding concepts I used.) The core code that computes Φ is simpler. I'll share that next.

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  16. 16. pro 2019.

    Every stats student gets to know the standard normal table. But, who needs a table when you can program a computer to do the on the fly? In this thread, I'll share code for two methods: Simpson's rule and Taylor series. Either would make a great student project!

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  17. 12. pro 2019.

    I’ve tweeted the benefits of including in class; soon I'll tweet the benefits of including probability. Teaser: students can make their own Z table using Taylor series! MY SAMPLE PROGRAM: You can interact with it !

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  18. 11. pro 2019.

    : Check out this little-known geometric derivation of the Maclaurin series for cosine and sine, animated by ! Looking forward to the forthcoming proof.

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  19. 3. pro 2019.

    QUESTION FOR MATH TEACHERS: Solving equations is a reasoning process, and standards correctly insist we teach this. Logical connective notation makes the reasoning explicit. It's concise and makes ideas like extraneous solutions feel natural! Would you teach this notation?

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  20. 27. stu 2019.

    Bitcoin uses , specifically geometric series, to model mining a finite resource: the first block contained a mining reward of 50 bitcoin, and this reward is halved every 210,000 blocks (~4 yrs). Can you solve for the long-run supply? Fig. by et al.

    Image taken from the book Bitcoin and Cryptocurrency Technologies by Narayanan et al.

Image shows three blocks in a hash chain, along with a hash tree of transactions from one of the blocks.
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  21. 25. stu 2019.
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