The Resource Extending the frontiers of mathematics : inquiries into proof and argumentation, Edward B. Burger

Extending the frontiers of mathematics : inquiries into proof and argumentation, Edward B. Burger

Label
Extending the frontiers of mathematics : inquiries into proof and argumentation
Title
Extending the frontiers of mathematics
Title remainder
inquiries into proof and argumentation
Statement of responsibility
Edward B. Burger
Creator
Subject
Language
eng
Cataloging source
YUS
http://library.link/vocab/creatorDate
1963-
http://library.link/vocab/creatorName
Burger, Edward B.
Illustrations
illustrations
Index
index present
LC call number
QA9.54
LC item number
.B87 2007
Literary form
non fiction
http://library.link/vocab/subjectName
  • Proof theory
  • Mathematical analysis
  • Logic, Symbolic and mathematical
Label
Extending the frontiers of mathematics : inquiries into proof and argumentation, Edward B. Burger
Instantiates
Publication
Note
Includes index
Contents
  • Juggling balls
  • Counting on a good hand and a good grade
  • Stepping back
  • 2.
  • Bringing theorems to justice : exposing the truth through rigorous proof
  • Making a statement
  • The
  • truth, the whole truth, and other stuff besides the truth
  • Arguing the case through proof
  • The
  • Introduction : a brief travel guide to the journey ahead
  • domino effect of bringing everyone down through guilt by induction
  • Stepping back
  • 3.
  • Delving into the dependable digits : counting on counting numbers
  • Divide and conquer
  • Solving equations by simple division
  • Now ready for prime time
  • Stepping back
  • 4.
  • Going around in circles : the art of modular arithmetic
  • To the student : a great adventure
  • The
  • mod side of mathematics
  • Old-school algebra gets an extreme makeover
  • The
  • power of congruences
  • Public secret codes
  • Stepping back
  • 5. The
  • irrational side of numbers : a world of nonrepeating digits
  • Divisible and indivisible
  • To the instructor : the mathematics to come
  • Forgoing fractions
  • Irrationalit-e
  • Stepping back --
  • 1.
  • Puzzles and patterns : a precursor to proofs
  • Senators and snakes
  • Checkerboards undercover
  • Flipping cards and coins
  • 7.
  • Infinity : understanding the unending
  • Comparing cardinality
  • Countable collections
  • The
  • return of power sets
  • A
  • pair of paradoxes
  • Stepping back
  • 8.
  • 6.
  • Recursively defined functions : the next generation
  • Moving ahead by looking back
  • Forgoing convergence - a formal look at power series
  • Generating closed formulas through generating functions
  • Stepping back
  • 9.
  • Discrete thoughts of counting : quantifying complicated quantities
  • Pigeons without a home
  • PERMUTATION = UP TO A REMINT
  • A
  • Discovering how to function in mathematics : moving beyond ordinary relations
  • combination that unlocks counting
  • Stepping back
  • 10.
  • Quantifying uncertainty with probability : a likely story?
  • What are the chances?
  • A
  • coin toss?
  • What's the deal?
  • Stepping back
  • 11. The
  • Get ready, get set
  • subtle art of connecting the dots : edging up to graphs
  • Bridging the graph
  • Making the circuit
  • Branching out to trees
  • Completely connected graphs
  • Stepping back --
  • Fun with functions
  • Moving onto an intimate one-to-one relationship with functions
  • An
  • intuitively-believable-yet-challenging-to-verify correspondence
  • Stepping back
  • Sizing up symmetry--
  • Keeping an artful eye on art galleries
  • Up, up, and away - the fourth dimension
  • Stepping back
  • 14. A
  • synergy between geometry and numbers : circles and Pythagorean triples
  • Rightful triangles
  • Determining which triangles are allright
  • A
  • rational look at the circle
  • 12.
  • Stepping back
  • 15. The
  • mathematical mysteries within a sheet of paper : unfolding pattern and structure
  • Getting into the fold
  • The
  • story unfolds
  • Adding arithmetic to generate a wild parity
  • Stepping back
  • 16.
  • Take it to the limit : an initial approach to analysis
  • Just plane graphs : drawing without being cross
  • Getting really close
  • Grasping the cloudlike Cantor set
  • Turning to ternary
  • Stepping back
  • 17.
  • Uninterrupted thoughts of continuity : a jump-free journey
  • Functions without lifting a finger
  • Valuing intermediate values
  • A
  • devilish staircase
  • Drawing without crossing
  • Stepping back --
  • Seemingly similar graphs
  • Sensing symmetry
  • Stepping back
  • 13.
  • Visible and invisible universes : geometric vignettes
  • Cycles and curves : algebraic structure in numbers and geometry
  • The
  • subculture of subgroups
  • Cyclic groups
  • A
  • circular group
  • Stepping back
  • 20.
  • Further frontiers
  • Appendix 1 : Hints, remarks, and leading questions
  • 18. An
  • Appendix 2 : A proof primer : the proof is in the pudding
  • 1.
  • Preproof prep
  • 2.
  • Penning the proof
  • 3.
  • Post proof
  • Appendix 3 : Commentary for instructors
  • How I used this material in my classroom
  • Appendix 4 : A math personality questionnaire
  • abstract world of algebra : reconciling with your x
  • Acknowledgments
  • Index
  • Grasping at groups
  • A
  • group mentality
  • Building a group table
  • Stepping back
  • 19.
Dimensions
23 cm.
Extent
xvi, 171 p.
Isbn
9781597570428
Lccn
20060457 29
Other physical details
ill.
System control number
  • (OCoLC)67922719
  • (OCoLC)67922719
Label
Extending the frontiers of mathematics : inquiries into proof and argumentation, Edward B. Burger
Publication
Note
Includes index
Contents
  • Juggling balls
  • Counting on a good hand and a good grade
  • Stepping back
  • 2.
  • Bringing theorems to justice : exposing the truth through rigorous proof
  • Making a statement
  • The
  • truth, the whole truth, and other stuff besides the truth
  • Arguing the case through proof
  • The
  • Introduction : a brief travel guide to the journey ahead
  • domino effect of bringing everyone down through guilt by induction
  • Stepping back
  • 3.
  • Delving into the dependable digits : counting on counting numbers
  • Divide and conquer
  • Solving equations by simple division
  • Now ready for prime time
  • Stepping back
  • 4.
  • Going around in circles : the art of modular arithmetic
  • To the student : a great adventure
  • The
  • mod side of mathematics
  • Old-school algebra gets an extreme makeover
  • The
  • power of congruences
  • Public secret codes
  • Stepping back
  • 5. The
  • irrational side of numbers : a world of nonrepeating digits
  • Divisible and indivisible
  • To the instructor : the mathematics to come
  • Forgoing fractions
  • Irrationalit-e
  • Stepping back --
  • 1.
  • Puzzles and patterns : a precursor to proofs
  • Senators and snakes
  • Checkerboards undercover
  • Flipping cards and coins
  • 7.
  • Infinity : understanding the unending
  • Comparing cardinality
  • Countable collections
  • The
  • return of power sets
  • A
  • pair of paradoxes
  • Stepping back
  • 8.
  • 6.
  • Recursively defined functions : the next generation
  • Moving ahead by looking back
  • Forgoing convergence - a formal look at power series
  • Generating closed formulas through generating functions
  • Stepping back
  • 9.
  • Discrete thoughts of counting : quantifying complicated quantities
  • Pigeons without a home
  • PERMUTATION = UP TO A REMINT
  • A
  • Discovering how to function in mathematics : moving beyond ordinary relations
  • combination that unlocks counting
  • Stepping back
  • 10.
  • Quantifying uncertainty with probability : a likely story?
  • What are the chances?
  • A
  • coin toss?
  • What's the deal?
  • Stepping back
  • 11. The
  • Get ready, get set
  • subtle art of connecting the dots : edging up to graphs
  • Bridging the graph
  • Making the circuit
  • Branching out to trees
  • Completely connected graphs
  • Stepping back --
  • Fun with functions
  • Moving onto an intimate one-to-one relationship with functions
  • An
  • intuitively-believable-yet-challenging-to-verify correspondence
  • Stepping back
  • Sizing up symmetry--
  • Keeping an artful eye on art galleries
  • Up, up, and away - the fourth dimension
  • Stepping back
  • 14. A
  • synergy between geometry and numbers : circles and Pythagorean triples
  • Rightful triangles
  • Determining which triangles are allright
  • A
  • rational look at the circle
  • 12.
  • Stepping back
  • 15. The
  • mathematical mysteries within a sheet of paper : unfolding pattern and structure
  • Getting into the fold
  • The
  • story unfolds
  • Adding arithmetic to generate a wild parity
  • Stepping back
  • 16.
  • Take it to the limit : an initial approach to analysis
  • Just plane graphs : drawing without being cross
  • Getting really close
  • Grasping the cloudlike Cantor set
  • Turning to ternary
  • Stepping back
  • 17.
  • Uninterrupted thoughts of continuity : a jump-free journey
  • Functions without lifting a finger
  • Valuing intermediate values
  • A
  • devilish staircase
  • Drawing without crossing
  • Stepping back --
  • Seemingly similar graphs
  • Sensing symmetry
  • Stepping back
  • 13.
  • Visible and invisible universes : geometric vignettes
  • Cycles and curves : algebraic structure in numbers and geometry
  • The
  • subculture of subgroups
  • Cyclic groups
  • A
  • circular group
  • Stepping back
  • 20.
  • Further frontiers
  • Appendix 1 : Hints, remarks, and leading questions
  • 18. An
  • Appendix 2 : A proof primer : the proof is in the pudding
  • 1.
  • Preproof prep
  • 2.
  • Penning the proof
  • 3.
  • Post proof
  • Appendix 3 : Commentary for instructors
  • How I used this material in my classroom
  • Appendix 4 : A math personality questionnaire
  • abstract world of algebra : reconciling with your x
  • Acknowledgments
  • Index
  • Grasping at groups
  • A
  • group mentality
  • Building a group table
  • Stepping back
  • 19.
Dimensions
23 cm.
Extent
xvi, 171 p.
Isbn
9781597570428
Lccn
20060457 29
Other physical details
ill.
System control number
  • (OCoLC)67922719
  • (OCoLC)67922719

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