MATH125- Midterm Exam Guide - Comprehensive Notes for the exam ( 108 pages long!)

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

1. 1 the geometry and algebra of vectors: vectors in the plane. One of the main concept in mathematics is the notion of a real num- ber. You know from high school that we can add, subtract, multiply and divide real numbers. The set of real numbers is denoted by r. In this course we introduce another important concept of vectors (and also vector spaces) which is (in a broad meaning) a generalization of the concept of real numbers. The primary aim of this course is rst to introduce the notion of a vector space and then to study their proper- ties. It is worth mentioning that vector spaces appear everywhere: in technology, science, engineering and etc. We are going to come to this natural notion through preliminary studying of vectors in the plane. We begin by considering the cartesian plane with the familiar x and y-axes. Thus, every point on the plane has two coordinates: x- coordinate and y-coordinate.