I have so wanted such resources for years. I have found some and should make a list.
The first time the difference between understanding some math, and understanding what the math meant, was after high school Trig. The moment I started manually programming graphics from scratch, the circle as a series of dots, trigonometry transformed in my mind. I can't even say what the difference was - the math was exactly the same - but some larger area of my brain suddenly connected with all the concepts I had already learned.
While ordering the "Mathematica: A Secret World of Intuition and Curiosity" I came across these books, which looked very promising in the "learning formal math by expanding intuition" theme, so I bought them too:
Field Theory For The Non-Physicist, by Ville Hirvonen [0]
Lagrangian Mechanics For The Non-Physicist, by Ville Hirvonen [1]
The Gravity of Math: How Geometry Rules the Universe, by Steve Nadis, Shing-Tung Yau [2]
Vector: A Surprising Story of Space, Time, and Mathematical Transformation, by Robyn Arianrhod [3]
[0] https://www.amazon.com/dp/B0CN7HMTJN
[1] https://www.amazon.com/dp/B0CN7HMK38
[2] https://www.amazon.com/dp/1541604296
[3] https://www.amazon.com/dp/0226821102
Excited to read each (based on their synopses & ratings), and if I will get compounding fluency across both math and physics between all five books.
The first time the difference between understanding some math, and understanding what the math meant, was after high school Trig. The moment I started manually programming graphics from scratch, the circle as a series of dots, trigonometry transformed in my mind. I can't even say what the difference was - the math was exactly the same - but some larger area of my brain suddenly connected with all the concepts I had already learned.
While ordering the "Mathematica: A Secret World of Intuition and Curiosity" I came across these books, which looked very promising in the "learning formal math by expanding intuition" theme, so I bought them too:
Field Theory For The Non-Physicist, by Ville Hirvonen [0]
Lagrangian Mechanics For The Non-Physicist, by Ville Hirvonen [1]
The Gravity of Math: How Geometry Rules the Universe, by Steve Nadis, Shing-Tung Yau [2]
Vector: A Surprising Story of Space, Time, and Mathematical Transformation, by Robyn Arianrhod [3]
[0] https://www.amazon.com/dp/B0CN7HMTJN
[1] https://www.amazon.com/dp/B0CN7HMK38
[2] https://www.amazon.com/dp/1541604296
[3] https://www.amazon.com/dp/0226821102
Excited to read each (based on their synopses & ratings), and if I will get compounding fluency across both math and physics between all five books.