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f2006lecNotesWeek01

# f2006lecNotesWeek01 - 2 2.1 Getting Started Set Basics...

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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

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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 ,...
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f2006lecNotesWeek01 - 2 2.1 Getting Started Set Basics...

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