I'm currently an online student working towards a mathematics degree. I've always had a knack for math, but I've only recently started applying that knack.
So far, I've been coding my higher order mathematics problems in Python using a Google Colabs environment. I usually use the Sympy library, but now that I'm getting deeper into the weeds with Calc II and differential equations, I'm starting to use Numpy and Scipy as well. Also, my "online tutor" so far is GPT-4. It isn't perfect, and sometimes I have to go back and forth if there's something that it's having difficulty with, but it works great 85% of the time.
As for understanding the concept of mathematics itself, I've found the books of David Berlinski to be invaluable, specifically "A Tour of the Calculus", but all his books on mathematics are incredibly illuminating. I have yet to read something he puts out where I don't learn something or see a topic in a different light.
I second the recommendation for Isaac Asimov. His non-fiction was a crucial factor in my intellectual development, particularly his essay collections. Do you know if they're still available?
I've found paperbacks of Azimov's "science fact" works (such as "Of Time and Space and Other Things" and "Science, Numbers, and I" on the used book market and digital copies to borrow at Internet Archive.
Now I'm not a mathematician but I do enjoy a good math book.
Mathematics It's Content Methods and Meaning by A.D. Aleksandrov et al is a good survey. It's a Dover book so you know it's a classic.
Another good survey is A Programmer's Introductio to Mathematics by Jeremy Kun. It covers much of the same material but is more calculation oriented.
If you don't have a math professor handy or your school has fired their friendly one A Handbook of Mathematical Discourse by Charles Wells is okay. This is more of a dictionary than anything else. But useful if you miss something is lecture and you're too embarrassed to ask later.
On this theme, I recommend A Mind for Numbers by Barbara Oakely. The author is a former US Army linguist who obtained her PhD in engineering in her thirties. The book covers learning tactics and strategies for those of us who struggled in math class.
I was taught a groat was fourpence, which makes a groat 1/5th of a shilling, and there are therefore there are 105 greats to a Guinea. I must ask the author to show his work.
I'm currently an online student working towards a mathematics degree. I've always had a knack for math, but I've only recently started applying that knack.
So far, I've been coding my higher order mathematics problems in Python using a Google Colabs environment. I usually use the Sympy library, but now that I'm getting deeper into the weeds with Calc II and differential equations, I'm starting to use Numpy and Scipy as well. Also, my "online tutor" so far is GPT-4. It isn't perfect, and sometimes I have to go back and forth if there's something that it's having difficulty with, but it works great 85% of the time.
As for understanding the concept of mathematics itself, I've found the books of David Berlinski to be invaluable, specifically "A Tour of the Calculus", but all his books on mathematics are incredibly illuminating. I have yet to read something he puts out where I don't learn something or see a topic in a different light.
I second the recommendation for Isaac Asimov. His non-fiction was a crucial factor in my intellectual development, particularly his essay collections. Do you know if they're still available?
I just wrote a post with some of my own book recommendations, here: https://aetherczar.substack.com/p/reading-list-for-chapter-1-on-generation
I've found paperbacks of Azimov's "science fact" works (such as "Of Time and Space and Other Things" and "Science, Numbers, and I" on the used book market and digital copies to borrow at Internet Archive.
Ah the memories of reading all those in junior high school.
I need to make a systematic effort to reacquire them.
Now I'm not a mathematician but I do enjoy a good math book.
Mathematics It's Content Methods and Meaning by A.D. Aleksandrov et al is a good survey. It's a Dover book so you know it's a classic.
Another good survey is A Programmer's Introductio to Mathematics by Jeremy Kun. It covers much of the same material but is more calculation oriented.
If you don't have a math professor handy or your school has fired their friendly one A Handbook of Mathematical Discourse by Charles Wells is okay. This is more of a dictionary than anything else. But useful if you miss something is lecture and you're too embarrassed to ask later.
On this theme, I recommend A Mind for Numbers by Barbara Oakely. The author is a former US Army linguist who obtained her PhD in engineering in her thirties. The book covers learning tactics and strategies for those of us who struggled in math class.
I stand corrected. 12 pence to the shilling, not 20.
I was taught a groat was fourpence, which makes a groat 1/5th of a shilling, and there are therefore there are 105 greats to a Guinea. I must ask the author to show his work.
As a shilling equalled twelve pence, three groats made a shilling.