Links between sub-fields of mathematics

[NotGauss]

Hello all!
Today I was in my vector calculus course (as a student) and we were learning about/calculating the unit tangent vector (T(t)) and principal unit normal vector(N(t)). We calculated T(1) and then moved onto N(1), ((1) our arbitrary point to see how it plays out). Nevertheless, after calculating N(1) with way too much algebra in my point of view and being told that/realizing that N(1) is orthogonal to T(1), I though "hey! i just did this in linear algebra and it took about 1/10th of the time and calculations by using transformations", and blurted this out in class. ( insert, smile from math teach, rumbles about linear algebra from fellow students that had to learn dets in calculus)
So, getting closer to the point,in the past two weeks I read Love and Math by Edward Frenkel and Fermat's Enigma by Simon Singh, which in both books stressed the actual and possibility of interconnected sub-fields of mathematics. So without further delay, what are some additional connections that would be interesting to an undergrad mathematics student such as myself? Excluded the beauties of analytical geometry...of course.

Thanks for your time and help,
Jon

P.S. I was not sure if "General Math" was the correct spot for this posting, but it seemed logical. If not please move to correct forum.

 

[Mark44]

There are some strong connections between linear algebra and differential equations, including the similarity between vector spaces and function spaces. The concepts of basis and spanning sets are present in both areas, as are the concepts of kernel, linear independence/dependence, and others.

 

[NotGauss]

Mark,
Thank you for the reply, I'll start looking into this over the coming weeks. Would you recommend any book, articles, text or just general GTS?