Mark Thornber

All readable. Pick the one where you have the least background:
The Mathematical Theory of The Top Felix Klein
Prime Numbers and the Riemann Hypothesis Barry Mazur
Random Walks and Electric Networks Doyle & Snell
The Mathematics of Medical Imaging Timothy Feeman

The group of unit quaternions (isomorphic to the matrix group SU(2)) is used extensively in modern 3D computer graphics. The sort used in all those games your students play when they should be doing FM homework.

#FridayFive
1. Tom Dooley - Doc Watson
2. I Don’t Like Mondays - The Boomtown Rats
3. Jean - Oliver
4. Lucky - Britney Spears
5. Cherry Bomb - The Runaways

Autocorrect seems to have added 0.000977… !

To solve:
First note eq3/eq1 gives 1/32=α^2r^3 so we do need the positive root after all!
Now eq2 divided by this gives
35/4=(1+r+2r^2+r^3+r^4)/r^2
This rearranges to a quartic and the factor theorem quickly gives r=2 etc.

The second equation is wrong. It needs α^2.
The fourth equation should be 1/1024=0.000977α^4r^6
(Is it obvious that we need the positive root?)

Ford Econoline -Nanci Griffith
By The Time I Get To Phoenix - Glen Campbell
Piss Factory - Patti Smith
Arthur’s Theme - Christopher Cross
I’ll Follow The Sun - The Beatles
#FridayFive

It can! Consider f(x,y)=ax^2+2bxy+cy^2.
fxx=2a fxy=2b and fyy=2c, so all values are possible.
This has a sta. pt. at the origin. The sign of b^2-ac tells you if z=f(x,y) is a parabolic or hyperboloid.

“Sing epsilon delta, Stewart and Tall” (Google it!)

Graham Cumming posted a long thread on X today, with his best guesses as to what went wrong and why things turned out as badly as they did. I suspect he is right on all counts!

#FridayFive
1. Long Hot Summer - Tom Robinson Band
2. I Am A Town - Mary Chapin Carpenter
3. Here Comes the Sun - The Beatles
4. If You Can’t Stand The Heat - Bucks Fizz
5. Summer Breeze - The Isley Brothers

OCR follows Rudin etc.
Item 8.01c on the specification states:
‘“Divergence” can refer to sequences that are bounded or unbounded.’

I don’t think this is correct. Here is professor Peter Coles (a Newcastle lad) with the original Latin and the translations.
https://telescoper.blog/2019/11/13/newtons-laws-in-translation/

This list worked for me
https://bhi.co.uk/repairer/

Are cointerior angles really equal?

Out Now: 'A Tribute to Nick Lord' celebrating his work within the Mathematical Gazette and his contributions to the MA. Printed copies from £7, with the eBook free to MA members, or for just £1 to non-members.

Printed: members.m-a.org.uk/Shop/product...
eBook: members.m-a.org.uk/Shop/product...

For polynomials, tangent lines can be found by looking for repeated roots. No need for limits.
We find m so that p(x)-p(a)=m(x-a) has a repeated root.
This gives m=p’(a)
For quadratics it’s good old b^2-4ac=0

It’s definitely a US thing. Just check any of their doorstep-sized textbooks.
I always thought it was easier to remember than concave/convex, but confusion arises later when convex is used to mean “the curve is under the chord”

There are a number of similar triangles. The ratios of corresponding lengths will be equal.

See my previous reply.

Lists are arrays. You can access individual items with indexing. For example L1[2]

I usually buy direct from the Double Two website. Lots of colours available
https://www.doubletwo.co.uk/mauve-long-sleeve-non-iron-cotton-rich-shirt/

The first 3 terms are (z-3)^2+1. Try the substitution u=z-3, followed by completing the square.

You should try the Guardian quick cryptic. Each one uses 4 different clue types and they give examples of each.

https://www.theguardian.com/crosswords/series/quick-cryptic

There’s a typo in 2a) …

#FridayFive
1. On the Dark Side - Eddy and the Cruisers
2. Power In The Darkness - Tom Robinson Band
3. Because the Night - Patti Smith
4. Corcovado (Quiet Nights of Quiet Stars) - Getz, Gilberto
5. Dancing In The Dark - Cannonball Adderley

We have seen issues with this in the past. Some courses at some universities want to make offers on 3 A levels taken at the same time. Medicine has been a problem here.

I do this in Excel
1) create a scatter graph with a single point
2) use series properties to make the point invisible
3) use axis properties to get scales and labels correct
4) use major and minor grid line properties to get the grid lines looking nice
You can export to Word

#FridayFive
1. The Only Living Boy in New York - Simon and Garfunkel
2. My Friend Stan - Slade
3. Whatever Happened To You - Highly Likely
4. There’s a Light Beyond These Woods (Mary Margaret) - Nanci Griffith
5. Woody and Dutch on the Slow Train to Peking - Rickie Lee Jones