Introduction To Abstract Mathematics

The book first offers information on logic and set theory natural numbers and integers and rational numbers.

Introduction to abstract mathematics. In algebra which is a broad division of mathematics abstract algebra occasionally called modern algebra is the study of algebraic structures. Description introduction to abstract mathematics focuses on the principles approaches and operations involved in abstract mathematics including metric spaces sets axiom systems and open sentences. Math 3000 introduction to abstract mathematics spring 2010 instructor. 1developing the skills necessary to read and practice abstract mathematics.

The reader is not overwhelmed by exotic topics that are rarely used but is introduced to abstract basic principles needed to understand other courses like for instance quantum mechanicsmore advanced graduate courses in algebra or functional analysis. Chapters 1 5 introduce the fundamentals of abstract mathematics and chapters 6 8 apply the ideas and techniques placing the earlier material in a real context. This course teaches a student how to construct logical arguments in the form of a proof to verify mathematical statements. If you ask someone on the street this question the most likely response will be.

Algebra is the abstract encapsulation of our intuition for composition. 11 introduction this book aims to bridge the gap between the mainly computation oriented lower division undergraduate classes and the abstract mathematics encountered in more advanced mathe matics courses. 1you will learn linear algebra which is one of the most widely used mathematical theories around. Something horrible to do with x y and z.

The book first offers information on logic and set theory natural numbers and integers and rational numbers. The goal of this book is threefold. Description introduction to abstract mathematics focuses on the principles approaches and operations involved in abstract mathematics including metric spaces sets axiom systems and open sentences. Readers interest is continually piqued by the use of clear explanations practical examples discussion and discovery exercises and historical comments.

If youre lucky enough to bump into a mathematician then you might get something along the lines of. Algebraic structures include groups rings fields modules vector spaces lattices and algebras. Ericsullivanatucdenveredu personal web address. Cu building room 631 cu building 6th floor 1250 14th st o ce phone.

Introduction to abstract mathematics is an online and individually paced college course taken after linear algebra and multivariable calculus. 3learning what sort of questions mathematicians ask what excites them and what they are.