Renaissance Math Curriculum

[DSKla]

I'm curious as to what areas of math a Renaissance mathematician would have been skilled in. Bonus points if you happen to know which actual texts they would have studied, or what modern curriculums would bring me up to that speed.

The reason is I never went very far in math, and I'm rusty on what I did learn. It's a bit embarassing to my competitive nature when my younger fiancee is solving all sorts of calculus problems for fun in her spare time and I can't remember how to calculate the area of basic geometric figures.

I don't have any pretensions of becoming great at it, but it seems like a reasonable goal to get about as good as a pre-Newtonian gentleman of mathematics over a period of a few years. To clarify, I don't need this for any particular purpose other than meeting the challenge of having a general understanding of basic maths that do not require more than pencil, paper, ruler, compass, protractor, etc.

Any recommendations are appreciated.

[ducknalddon]

My son used Engineering Mathematics by KA Stroud during his studies, it's got a nice progression of explanation followed by worked examples then exercises. You could start at the beginning and just work your way through it until you reach the end or are satisfied with your progress. I wish I had come across it when I started studying mathematics.

[Dragline]

I would use the free tutorials on Khan Academy website. Learn some probability and statistics if you don't know that already.

https://www.khanacademy.org/

[7Wannabe5]

I recently had to sit for a test of Basic Math Literacy in order to qualify for a job as a tutor. I wasn't sure whether the standard definition of Basic Math applied, so I did quick dirty review of Cliff's Pre-calculus. So, I can inform you with good deal of confidence that if you were to make your way through any collection of tutorials or review guides up to the level of pre-calculus, you will know much more math than necessary to tutor the topic in any affluent suburb of the United States.

The order of progress through the standard modern math curriculum does not follow the historical development of math. Applied math and abstract math are two very different animals. I don't see much point in memorizing formulas you rarely need to apply. More interesting to think about how if you were to spin randomly on a lazy susan and throw paint balls with a tireless arm for a very long time, eventually your friend sitting way up high in a tree might see a circle emerging from the pattern of the splotches. OTOH, a square is sort of tricky, because not part of God's kingdom.

Or, you could try to teach yourself to count and add/subtract from the perspective that instead of 10 fingers, you have 8 fingers and 2 thumbs. Works way better, IMO.

[George the original one]

There's nothing like the higher geometry (squaring circles, projections) and number theory* (commutative, distributive, what's this operator?) to exercise your mind without getting bogged down in calculus.

*obligatory sorry math nerd joke: what's purple and commutes? An abelian grape. (see https://en.wikipedia.org/wiki/Abelian_group)

[pukingRainbows]

My assumption is that you're interested in learning fundamental mathematics? And not specifically limiting yourself to the knowledge and theories of a certain time period?

I would suggest going down the rabbit hole of youtube videos and see where you end up. There is tonnes of useful information that is catered to all different levels.

I had a similar process trying to remember what differentials were and it was a lot more interesting the second time around through the magic of the internet and video. I started with a search for 'basic calculus explained' and went from there.

Good luck!

[DSKla]

Yes, fundamentals as opposed to time period, or in other words, things that can be used for more practical purposes without computer aid.

The khan academy site looks promising. Thanks for all the suggestions.