Oct 04, 2012 · In the past, linear algebra texts commonly made this transition abruptly. They began with extensive computations of linear systems, matrix multiplications, and determinants. When the concepts—vector spaces and linear maps—finally appeared, and definitions and proofs started, often the change brought students to a stop.
Just define R := P + Q and then take the dot product of each side with itself: R · R = P · P + 2 P · Q + Q · Q ( 7) where every term except 2 P · Q is manifestly a scalar, so the remaining term must be a scalar as well. This leaves us pretty much convinced that the dot product between any two vectors is a scalar.
Introduction to Abstract Algebra provides insight into the methods of abstract algebra. This book provides information pertinent to the fundamental concepts of abstract algebra. Organized into five chapters, this book begins with an overview of the study of natural numbers that are used historically for the purpose of counting the objects in ...
Aug 16, 2013 · applications of abstract algebra. A basic knowledge of set theory, mathe-matical induction, equivalence relations, and matrices is a must. Even more important is the ability to read and understand mathematical proofs. In this chapter we will outline the background needed for a course in abstract algebra. 1.1 A Short Note on Proofs
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) 4th ed. 2015 Edition. by David A. Cox (Author), John Little (Author), Donal O'Shea (Author) & 0 more. 5.0 out of 5 stars 10 ratings.
Introduction Overview Needs As We Go Through These Topics, We Will Pay Speciﬁc Attention To 1. Proof writing (standard proof methods) 2. Applications (digital circuits, scientiﬁc method, public key encryption) 3. Useful abstractions (it turns out that abstraction makes us more efﬁcient) 4. Proofs of results that are familiar from elementary through
Unit 2 - Reasoning and Proof. 2-1 Inductive and Deductive Reasoning. 2-2 Logic. 2-3 Proving Theorems. 2-4 Algebraic Proofs. 2-5 Theorems about Angles and Perpendicular Lines. 2-6 Planning a Proof. Inductive Reasoning - PDFs. 2-1 Assignment Student Edition - Inductive and Deductive Reasoning (FREE)
It has a lot more detail on stuff like floating point storage, memory layout, sparse matrices, iterative methods, etc than most linear algebra courses, but doesn't go much in to proofs, geometric interpretations, and other stuff that's less needed for algorithm design and implementation. (Disclaimer, I'm from fast.ai.)