{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}


f2006lecNotesWeek01 - 2 2.1 Getting Started Set Basics...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
2 Getting Started — Set Basics 2.1 Opening quote Mathematics may be defned as the subject in which we never know what we are talking about, nor whether what we are saying is true – Bertrand Russell 2.2 Outline of Course Foundations oF mathematics some understanding oF the structure oF math sets, logic, prooF techniques counting and probability relationship between these topics Functions and relations Focus on characteristics oF relations how are certain relations similar/different? matrices arrays oF values with operations on them graphs explain brie±y trees special category oF graphs 2.3 A Closer Look at Foundations any branch oF mathematics is based on: undefned terms, defnitions, assumptions, theorems an example From plane Euclidean geometry defnition oF a circle based on terms: set, point, plane ultimately, some terms must go undefned (see Russell) assumptions again From plane Euclidean geometry parallel postulate (see Russell again) theorems — concepts that can be proven using earlier items what do we mean by a prooF? based on logic we will spend some time on both logic and prooF 2.4 Introduction to Sets start with set and element as undefned terms but we have an intuitive notion oF what we mean set notation { and } use oF dots set membership use oF symbol use oF / sets containing sets 5
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
the empty set, use of {} for difference between and {∅} 2.5 Set Equality sets are equal if they contain the same elements order is immaterial examples repetition is ignored examples 2.6 Useful Sets and Properties some common sets Z + , Z nonneg , Z , Q , R fairly informal discussion of each note occasional use of N for { 1 , 2 , 3 ,...
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

f2006lecNotesWeek01 - 2 2.1 Getting Started Set Basics...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online