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I must disagree. In my experience Linear Algebra has been so much easier than Calculus because even though at times it can be very abstract it is still more fa
by pmalynin 12y ago
I must disagree.
In my experience Linear Algebra has been so much easier than Calculus because even though at times it can be very abstract it is still more familiar as most of the time you're just solving equations. My math professors have done quite a good job in connecting the two subjects. For example, differentiation and integration of polynomials can be expressed as a linear algebra problem, etc. etc.
"The fundamental theorem of calculus is a legitimately earth-shattering breakthrough: none of the theorems in linear algebra come anywhere near it in cultural importance."
Linear Algebra has the Fundamental Theorem of Algebra (i.e. every polynomial has a solution in the complex numbers) and also the Isomorphism Theorems that say all vector spaces of n-dimensions are the same. For example polynomials of the form c+bx are equivalent to the complex numbers (over the reals) which are equivalent to two-vectors (x,y). Quantum physics is basically linear algebra, with quantum states defined as vectors in a quantum vector-space.
Don't dismiss the impact of Linear Algebra.
- mafribe 12y agoIn what sense is the fundamental theory of algebra (FTA) a theorem of linear algebra? It's rarely proven in linear algebra courses. Most proofs of the FTA involve concepts from the analytical side of mathematics.