Jim Doherty

husband, dad, son, brother, math teacher, Mets fan, proud member of the #MTBoS, #iteachmath, music obsessive ( AKA DJ Calc)

[Jim Doherty @mrdardy]

@MathCurmudgeon The simplicity of it is, obviously, a major appeal. I am just trying to anticipate confusion and I wonder if being more diligent about the dy/dx notation might help offset that. Additionally, it might pay off when beginning antidifferentiation

[Jim Doherty @mrdardy]

This year, I am teaching AP Calc AB for the first time in a while. Thinking about implicit differentiation and I thinkI am going to really emphasize dy/dt notation more than y' as a way to ease the impicit differentiation challenge.

[Jim Doherty @mrdardy]

@mathillustrated I would love to hear some of them. I have been teaching BC for the past 14 years and we teach that as a second year class so this has not been much of an issue.

[Jim Doherty @mrdardy]

@KarenCampe This was shown to me by one of my colleagues. I have to admit I have never thought of applying FTC this way, but with our notation on integrals going to the left instead of right, I think this makes some sense

[Jim Doherty @mrdardy]

An interesting take on the FTC from a student at our school. Asked for the derivative of the integral of sqrt (t) from 4 to x^2, she identified three cases for the answer. A) 2 < |x| B) 2 = |x| C) |x| < 2

Is she overthinking it, or have I been underthinking FTC?

[Jim Doherty @mrdardy]

Trig question : for f(x) = A cos (bx) + C sin (dx) I know that the period is the LCM of the two component periods. Is there a way to find the amplitude? Is amplitude a logical question?

[Jim Doherty @DJCalc]

Tonight's show on https://t.co/GJgbDYR4XO is uploaded

Here - https://t.co/Z2NpuVm3NP

and here - https://t.co/iGynSYFHsS

Spotify Link - https://t.co/ikCyDnicu4

Playlist

[Jim Doherty @mrdardy]

@dmarain David can you give me some insight into why the (8-x+1)*(8 - y +1) formula gives me the number of x by y rectangles on the chessboard?

[Jim Doherty @mrdardy]

In Calc BC yesterday I posted a picture of a chessboard and asked for how many squares there would be. We worked our way through to the answer. I then posed the question of how many x by y rectangles there would be. One student proposed (8-x+1)*(8-y+1)
1/2

[Jim Doherty @mrdardy]

@dmarain He proposed one! (Sum of 1 to m (sum on 1 to n (m-x+1) (n- y + 1)) for rectangles of dimension x by y.

[Jim Doherty @mrdardy]

A quick check seems to confirm this. Are these formulas ones any of you have seen before? He could not really explain his insight comfortably.

3/2

[Jim Doherty @mrdardy]

His formula seems to check. Someone else then asked about the number of rectangles is the original size was not 8 by 8 but, instead, an m by n rectangle. My student who proposed the original formula thinks this is a sum of sigma 1 to m of (m-x+1) and sigma 1 to n of (n-y+1)
2/2

[Jim Doherty @DJCalc]

Tonight's show uploaded here - https://t.co/pUg7qtjV6d

and here - https://t.co/daTALaAzgX

Spotify Link - https://t.co/kZF4W1Zu2H

Playlist

[Jim Doherty @DJCalc]

Tonight's show uploaded here - https://t.co/0lXNueJZ6O

and here - https://t.co/VaOJvDLGoA

Spotify Link - https://t.co/sDeT2ZNsXb

Tonight's Playlist

[Jim Doherty @DJCalc]

Tonight's show uploaded here - https://t.co/fTvolT9K0O

and here - https://t.co/MKPOEyGEPU

Spotify Link - https://t.co/PY8I2k3vw5

Tonight's Playlist

[Jim Doherty @DJCalc]

For my show tonight on https://t.co/GJgbDYRCNm (7 - 9 PM ET) I shine a spotlight on The Bats (new album!) and feature @voxtrot @nadasurf @AmyRigby and new tunes by @cuddlemagic , Melody Chambers, Bruiser and Bicycle, and 16 others. You can stream from our site, so drop on by!

[Jim Doherty @mrdardy]

@HarMath @dmarain Fred - thanks for the reply. I am trying to remember where I found this question or what I was thinking when I assigned it. What tip could I give to my students about thinking of the 75th term?

[Jim Doherty @mrdardy]

@HarMath @dmarain
I wrote a HW problem and I cannot remember what I was thinking when I wrote it! Consider the sequence: 24, 37, 40, 63, 66, ...
a) Is this arithmetic, geometric, or neither?
b) Is 189 in the sequence?
c) What is the 75th term in the sequence?
Any elegant ideas?

[Jim Doherty @DJCalc]

Tonight's show wrap

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and here - https://t.co/xLbJEQifHu

Spotify - https://t.co/AGljjIaRxS

Playlist

[Jim Doherty @mrdardy]

@HarMath @dmarain @howie_hua @decompwlj @RaminKhosravi4 @sonukg4india @jamestanton @mATH_e_matics @MathCurmudgeon @pickover Wild guessing here looking for a generalization. 13/999 is repeating 13 in base 10 (9 is one less than 10)
21 repeating in base 3 is 21/22 (2 is one less than 3)
How about something like 23 repeating in base 4? Is it 23/33 (3 is one less than 4) ?