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Mathematics research for the beginning student . Volume 1. : accessible projects for students before calculus / / edited by Eli E. Goldwyn, Sandy Ganzell and Aaron Wootton
Mathematics research for the beginning student . Volume 1. : accessible projects for students before calculus / / edited by Eli E. Goldwyn, Sandy Ganzell and Aaron Wootton
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (323 pages)
Disciplina 510
Collana Foundations for Undergraduate Research in Mathematics
Soggetto topico Mathematics - Research
Investigació matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-031-08560-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Games on Graphs: Cop and Robber, Hungry Spiders, and Broadcast Domination -- 1 Introduction -- 2 The Game of Cops and Robbers -- 3 Hungry Spiders -- 4 (t,r) Broadcast Domination -- 5 Further Investigation -- 6 A Short Primer on Graph Theory -- References -- Mathematics for Sustainable Humanity: Population, Climate, Energy, Economy, Policy, and Social Justice -- 1 Introduction -- 2 Quantifying Change -- 2.1 Absolute and Relative Change and Rate of Change -- 2.2 Linear and Exponential Change -- 2.3 Measuring and Estimating -- 3 Population Growth and Ecological Footprint -- 4 Climate Change -- 5 Energy Production, Consumption, and Efficiency -- 6 Economic Growth (and Collapse) -- 7 Policy and Social Justice -- References -- Mosaics and Virtual Knots -- 1 Math and Knots -- 2 Gauss Codes -- 3 Virtual Knots -- 4 Mosaics -- 5 Virtual Mosaics -- 6 Further Reading -- References -- Graph Labelings: A Prime Area to Explore -- 1 Introduction -- 1.1 Families and Classes of Graphs -- 1.2 Graph Operations -- 1.3 Introduction to Graph Labeling -- 2 Coprime and Prime Labelings -- 2.1 Minimal Coprime Labeling -- 3 Consecutive Cyclic Prime Labelings -- 4 Neighborhood-Prime Labelings -- 4.1 Building on Cycles -- 4.2 Building on Trees -- 4.2.1 Further Projects on Neighborhood-Prime Labelings -- 5 Conclusion -- References -- Acrobatics in a Parametric Arena -- 1 Analogies to Motivate Parametric Thinking -- 2 Overview -- 3 Parametric Basics -- 3.1 Parametric Function 1 -- 3.2 Parametric Function 2 -- 3.3 Parametric Function 3 -- 4 Function Concepts -- 4.1 Functions and Nonfunctions, Based on the Context -- 4.2 Connecting Component Functions and the Parametric Function -- 5 Try Some Parametric Acrobatics Yourself -- 5.1 General Desmos Graphing Instructions -- 5.2 Exercises with some Desmos Instructions -- 5.3 Experimentation.
6 True Acrobatics: Parametric Modeling of a Flower Stick -- 6.1 Flower Sticks and Digitized Motion -- 6.2 Modeling the Left End of the Flower Stick -- 6.3 More on the Flower Stick -- 6.4 Your Work -- 7 Financial Acrobatics: Modeling US Wireless Subscribers -- 7.1 About the Data -- 7.2 Views of the Data -- 7.3 Data Projections -- 7.4 Linear Fits to 2004-2014 Data -- 7.5 Proportional Growth -- 8 GeoGebra to Practice 3D Parametric Equation -- 9 Your Project -- References -- Further Reading -- Software -- But Who Should Have Won? Simulating Outcomes of Judging Protocols and Ranking Systems -- 1 Introduction -- 2 Fundamentals of Probability -- 2.1 A Little Set Theory -- 2.2 Computing Probability -- 2.3 Conditional Probability -- 2.4 Random Variables and Probability Functions -- 2.4.1 Discrete Random Variables -- 2.4.2 Continuous Random Variables -- 3 Introduction to Simulation -- 3.1 Random Number Generation -- 3.1.1 Sampling from Discrete Distributions -- 3.1.2 Sampling from Continuous Distributions -- 3.2 ``If/Else'' Statements -- 3.3 ``While'' and ``For'' Loops -- 3.3.1 ``While'' Loops -- 3.3.2 ``For Loops'' -- 3.4 Writing More Complex Simulation Code -- 4 Suggested Research Projects -- 4.1 Scenario 1: Objective Ranking -- 4.2 Scenario 2: Subjective Ranking -- 4.3 Scenario 3: Comparing Voting Methods -- References -- Modeling of Biological Systems: From Algebra to Calculus and Computer Simulations -- 1 Introduction -- 1.1 A Description of Mathematical Modeling -- 1.2 Building a Model with Bias -- 1.3 A Note About Computer-Based Simulations -- 1.4 Active Learning -- 2 Grey Squirrels in Six Fronts Park: Modeling a Changing Population -- 2.1 The Problem -- 2.1.1 Step 1: Goals, Questions, and Assumptions -- 2.1.2 Step 2: Build a Model -- 2.1.3 Step 3. Apply the Model -- 2.1.4 Step 4. Assess and Revise Your Model -- 2.2 Conclusion and Exercises.
3 Non-contact Cardiovascular Measurements -- 3.1 Context -- 3.2 The Challenge -- 3.3 The Initial Experiment -- 3.4 Weigh a Bed? -- 3.5 Let Us Get Our Hands Dirty! -- 3.6 Interesting Observations -- 3.7 Conclusions -- 4 Difference Equations in Population Ecology -- 4.1 Introduction -- 4.2 Population Growth with Difference Equations -- 4.3 Coding Difference Equations -- 4.4 Difference Equations for Predator-Prey Problems -- 5 Modeling the Spread of Infectious Diseases with Differential Equations -- 5.1 Modeling the Demise of Candy -- 5.2 Population Growth Models in Continuous Time -- 5.2.1 A Basic Model of Infectious Disease Spread -- 5.3 Discussion -- 6 Conclusions -- References -- Population Dynamics of Infectious Diseases -- 1 Mathematical Models in Epidemiology -- 2 An Individual-Based Epidemic Model -- 2.1 Model Description and Physical Simulation -- 2.2 Computer Simulation -- 2.3 Section 2 Exercises -- 2.4 Section 2 Challenge Problem -- 2.5 Section 2 Projects -- 3 Continuous-Time Dynamical Systems -- 3.1 The Derivative -- 3.2 Dynamical Systems -- 3.3 Section 3 Exercises -- 4 Dynamical System Models -- 4.1 Classification of Dynamical System Models -- 5 Building the SEIR Epidemic Model -- 5.1 Quantifying the Processes -- 5.1.1 Transition Processes -- 5.1.2 The Transmission Process -- 5.2 The Final Model -- 5.3 Section 5 Exercises -- 6 Modeling -- 6.1 Identifying Parameter Values -- 6.2 The Basic Reproduction Number -- 6.3 Section 6 Exercises -- 6.4 Section 6 Challenge Problem -- 7 Model Analysis -- 7.1 Early Phase Exponential Growth -- 7.2 The End State -- 7.3 Section 7 Exercises -- 7.4 Section 7 Challenge Problems -- 7.5 Section 7 Project -- 8 Simulations -- 8.1 Numerical Simulation of Continuous Dynamical Systems -- 8.2 Implementation of Numerical Simulations -- 8.3 Section 8 Exercises -- 8.4 Section 8 Projects -- Appendix: Programs -- hpsr.m.
HPSR_onesim.m -- HPSR_avg.m -- seir.m -- SEIR_onesim.m -- SEIR_comparison.m -- SEIR_paramstudy.m -- References -- Playing with Knots -- 1 Knots: Knotted and Unknotted -- 1.1 What Is a Knot? (The Basics) -- 1.2 Knot Equivalence and Reidemeister Moves -- 1.3 Some Useful Knots and Links -- 1.4 Unknotting Operations and Numbers -- 1.5 Knot Invariants -- 2 The Knotting-Unknotting Game -- 3 The Region Unknotting Game -- 4 The Linking-Unlinking Game -- 5 The KnotLink Game -- 6 The Link Smoothing Game -- 7 Conclusion -- References.
Record Nr. UNINA-9910632484403321
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Mathematics research for the beginning student . Volume 1. : accessible projects for students before calculus / / edited by Eli E. Goldwyn, Sandy Ganzell and Aaron Wootton
Mathematics research for the beginning student . Volume 1. : accessible projects for students before calculus / / edited by Eli E. Goldwyn, Sandy Ganzell and Aaron Wootton
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (323 pages)
Disciplina 510
Collana Foundations for Undergraduate Research in Mathematics
Soggetto topico Mathematics - Research
Investigació matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-031-08560-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Games on Graphs: Cop and Robber, Hungry Spiders, and Broadcast Domination -- 1 Introduction -- 2 The Game of Cops and Robbers -- 3 Hungry Spiders -- 4 (t,r) Broadcast Domination -- 5 Further Investigation -- 6 A Short Primer on Graph Theory -- References -- Mathematics for Sustainable Humanity: Population, Climate, Energy, Economy, Policy, and Social Justice -- 1 Introduction -- 2 Quantifying Change -- 2.1 Absolute and Relative Change and Rate of Change -- 2.2 Linear and Exponential Change -- 2.3 Measuring and Estimating -- 3 Population Growth and Ecological Footprint -- 4 Climate Change -- 5 Energy Production, Consumption, and Efficiency -- 6 Economic Growth (and Collapse) -- 7 Policy and Social Justice -- References -- Mosaics and Virtual Knots -- 1 Math and Knots -- 2 Gauss Codes -- 3 Virtual Knots -- 4 Mosaics -- 5 Virtual Mosaics -- 6 Further Reading -- References -- Graph Labelings: A Prime Area to Explore -- 1 Introduction -- 1.1 Families and Classes of Graphs -- 1.2 Graph Operations -- 1.3 Introduction to Graph Labeling -- 2 Coprime and Prime Labelings -- 2.1 Minimal Coprime Labeling -- 3 Consecutive Cyclic Prime Labelings -- 4 Neighborhood-Prime Labelings -- 4.1 Building on Cycles -- 4.2 Building on Trees -- 4.2.1 Further Projects on Neighborhood-Prime Labelings -- 5 Conclusion -- References -- Acrobatics in a Parametric Arena -- 1 Analogies to Motivate Parametric Thinking -- 2 Overview -- 3 Parametric Basics -- 3.1 Parametric Function 1 -- 3.2 Parametric Function 2 -- 3.3 Parametric Function 3 -- 4 Function Concepts -- 4.1 Functions and Nonfunctions, Based on the Context -- 4.2 Connecting Component Functions and the Parametric Function -- 5 Try Some Parametric Acrobatics Yourself -- 5.1 General Desmos Graphing Instructions -- 5.2 Exercises with some Desmos Instructions -- 5.3 Experimentation.
6 True Acrobatics: Parametric Modeling of a Flower Stick -- 6.1 Flower Sticks and Digitized Motion -- 6.2 Modeling the Left End of the Flower Stick -- 6.3 More on the Flower Stick -- 6.4 Your Work -- 7 Financial Acrobatics: Modeling US Wireless Subscribers -- 7.1 About the Data -- 7.2 Views of the Data -- 7.3 Data Projections -- 7.4 Linear Fits to 2004-2014 Data -- 7.5 Proportional Growth -- 8 GeoGebra to Practice 3D Parametric Equation -- 9 Your Project -- References -- Further Reading -- Software -- But Who Should Have Won? Simulating Outcomes of Judging Protocols and Ranking Systems -- 1 Introduction -- 2 Fundamentals of Probability -- 2.1 A Little Set Theory -- 2.2 Computing Probability -- 2.3 Conditional Probability -- 2.4 Random Variables and Probability Functions -- 2.4.1 Discrete Random Variables -- 2.4.2 Continuous Random Variables -- 3 Introduction to Simulation -- 3.1 Random Number Generation -- 3.1.1 Sampling from Discrete Distributions -- 3.1.2 Sampling from Continuous Distributions -- 3.2 ``If/Else'' Statements -- 3.3 ``While'' and ``For'' Loops -- 3.3.1 ``While'' Loops -- 3.3.2 ``For Loops'' -- 3.4 Writing More Complex Simulation Code -- 4 Suggested Research Projects -- 4.1 Scenario 1: Objective Ranking -- 4.2 Scenario 2: Subjective Ranking -- 4.3 Scenario 3: Comparing Voting Methods -- References -- Modeling of Biological Systems: From Algebra to Calculus and Computer Simulations -- 1 Introduction -- 1.1 A Description of Mathematical Modeling -- 1.2 Building a Model with Bias -- 1.3 A Note About Computer-Based Simulations -- 1.4 Active Learning -- 2 Grey Squirrels in Six Fronts Park: Modeling a Changing Population -- 2.1 The Problem -- 2.1.1 Step 1: Goals, Questions, and Assumptions -- 2.1.2 Step 2: Build a Model -- 2.1.3 Step 3. Apply the Model -- 2.1.4 Step 4. Assess and Revise Your Model -- 2.2 Conclusion and Exercises.
3 Non-contact Cardiovascular Measurements -- 3.1 Context -- 3.2 The Challenge -- 3.3 The Initial Experiment -- 3.4 Weigh a Bed? -- 3.5 Let Us Get Our Hands Dirty! -- 3.6 Interesting Observations -- 3.7 Conclusions -- 4 Difference Equations in Population Ecology -- 4.1 Introduction -- 4.2 Population Growth with Difference Equations -- 4.3 Coding Difference Equations -- 4.4 Difference Equations for Predator-Prey Problems -- 5 Modeling the Spread of Infectious Diseases with Differential Equations -- 5.1 Modeling the Demise of Candy -- 5.2 Population Growth Models in Continuous Time -- 5.2.1 A Basic Model of Infectious Disease Spread -- 5.3 Discussion -- 6 Conclusions -- References -- Population Dynamics of Infectious Diseases -- 1 Mathematical Models in Epidemiology -- 2 An Individual-Based Epidemic Model -- 2.1 Model Description and Physical Simulation -- 2.2 Computer Simulation -- 2.3 Section 2 Exercises -- 2.4 Section 2 Challenge Problem -- 2.5 Section 2 Projects -- 3 Continuous-Time Dynamical Systems -- 3.1 The Derivative -- 3.2 Dynamical Systems -- 3.3 Section 3 Exercises -- 4 Dynamical System Models -- 4.1 Classification of Dynamical System Models -- 5 Building the SEIR Epidemic Model -- 5.1 Quantifying the Processes -- 5.1.1 Transition Processes -- 5.1.2 The Transmission Process -- 5.2 The Final Model -- 5.3 Section 5 Exercises -- 6 Modeling -- 6.1 Identifying Parameter Values -- 6.2 The Basic Reproduction Number -- 6.3 Section 6 Exercises -- 6.4 Section 6 Challenge Problem -- 7 Model Analysis -- 7.1 Early Phase Exponential Growth -- 7.2 The End State -- 7.3 Section 7 Exercises -- 7.4 Section 7 Challenge Problems -- 7.5 Section 7 Project -- 8 Simulations -- 8.1 Numerical Simulation of Continuous Dynamical Systems -- 8.2 Implementation of Numerical Simulations -- 8.3 Section 8 Exercises -- 8.4 Section 8 Projects -- Appendix: Programs -- hpsr.m.
HPSR_onesim.m -- HPSR_avg.m -- seir.m -- SEIR_onesim.m -- SEIR_comparison.m -- SEIR_paramstudy.m -- References -- Playing with Knots -- 1 Knots: Knotted and Unknotted -- 1.1 What Is a Knot? (The Basics) -- 1.2 Knot Equivalence and Reidemeister Moves -- 1.3 Some Useful Knots and Links -- 1.4 Unknotting Operations and Numbers -- 1.5 Knot Invariants -- 2 The Knotting-Unknotting Game -- 3 The Region Unknotting Game -- 4 The Linking-Unlinking Game -- 5 The KnotLink Game -- 6 The Link Smoothing Game -- 7 Conclusion -- References.
Record Nr. UNISA-996499869103316
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Mathematics research for the beginning student : accessible projects for students after calculus. / / edited by Eli E. Goldwyn, Sandy Ganzell, Aaron Wootton
Mathematics research for the beginning student : accessible projects for students after calculus. / / edited by Eli E. Goldwyn, Sandy Ganzell, Aaron Wootton
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (314 pages)
Disciplina 780
Collana Foundations for Undergraduate Research in Mathematics
Soggetto topico Mathematics - Research
Investigació matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-031-08564-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996499869403316
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Mathematics research for the beginning student : accessible projects for students after calculus. / / edited by Eli E. Goldwyn, Sandy Ganzell, Aaron Wootton
Mathematics research for the beginning student : accessible projects for students after calculus. / / edited by Eli E. Goldwyn, Sandy Ganzell, Aaron Wootton
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (314 pages)
Disciplina 780
Collana Foundations for Undergraduate Research in Mathematics
Soggetto topico Mathematics - Research
Investigació matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-031-08564-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910631092703321
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
A primer for undergraduate research : from groups and tiles to frames and vaccines / / edited by Aaron Wootton, Valerie Peterson, Christopher Lee
A primer for undergraduate research : from groups and tiles to frames and vaccines / / edited by Aaron Wootton, Valerie Peterson, Christopher Lee
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017
Descrizione fisica 1 online resource (313 pages) : illustrations
Disciplina 516.35
Collana Foundations for Undergraduate Research in Mathematics
Soggetto topico Discrete mathematics
Group theory
Number theory
Convex geometry 
Discrete geometry
Biomathematics
Matrix theory
Algebra
Discrete Mathematics
Group Theory and Generalizations
Number Theory
Convex and Discrete Geometry
Physiological, Cellular and Medical Topics
Linear and Multilinear Algebras, Matrix Theory
ISBN 3-319-66065-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Coxeter Groups and the Davis Complex (T.A. Schroeder) -- A Tale of Two Symmetries: Embeddable and Non-Embeddable Group Actions on Surfaces (V. Peterson, A. Wootton) -- Tile Invariants for Tackling Tiling Questions (M.P. Hitchman) -- Forbidden Minors: Finding the Finite Few (T.W. Mattman) -- Introduction to competitive graph coloring (C. Dunn, V. Larsen, J.F. Nordstrom) -- Matrioids (E. McNicholas, N.A. Neudauer, C. Starr) -- Finite Frame Theory (S. Datta, J. Oldroyd) -- Mathematical decision-making with linear and convex programming (J. Kotas) -- Computing weight multiplicities (P. E. Harris) -- Vaccination strategies for small worlds. (W. Just, H. C. Highlander) -- Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations (R. C. Harwood).
Record Nr. UNINA-9910279757403321
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
A Project-Based Guide to Undergraduate Research in Mathematics [[electronic resource] ] : Starting and Sustaining Accessible Undergraduate Research / / edited by Pamela E. Harris, Erik Insko, Aaron Wootton
A Project-Based Guide to Undergraduate Research in Mathematics [[electronic resource] ] : Starting and Sustaining Accessible Undergraduate Research / / edited by Pamela E. Harris, Erik Insko, Aaron Wootton
Edizione [1st ed. 2020.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020
Descrizione fisica 1 online resource (XI, 324 p. 142 illus., 81 illus. in color.)
Disciplina 510
Collana Foundations for Undergraduate Research in Mathematics
Soggetto topico Combinatorics
ISBN 3-030-37853-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Folding Words Around Trees: Models Inspired by RNA -- Phylogenic Networks -- Tropical Geometry -- Chip Firing Games and Critical Groups -- Counting Tilings by Taking Walks in a Graph -- Beyond Coins, Stamps, and Chicken McNuggets: an Invitation to Numerical Semigroups -- Lateral Movement in Undergraduate Research: Case Studies in Number Theory -- Projects in (t,r) Broadcast Domination -- Squigonometry: Trigonomtry in the p-norm -- Researching in Undergraduate Mathematics Education -- Possible Directions for Both Undergraduate Students and Faculty -- Undergraduate Research in Mathematical Epidemiology.
Record Nr. UNISA-996418196903316
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
A Project-Based Guide to Undergraduate Research in Mathematics : Starting and Sustaining Accessible Undergraduate Research / / edited by Pamela E. Harris, Erik Insko, Aaron Wootton
A Project-Based Guide to Undergraduate Research in Mathematics : Starting and Sustaining Accessible Undergraduate Research / / edited by Pamela E. Harris, Erik Insko, Aaron Wootton
Edizione [1st ed. 2020.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020
Descrizione fisica 1 online resource (XI, 324 p. 142 illus., 81 illus. in color.)
Disciplina 510
Collana Foundations for Undergraduate Research in Mathematics
Soggetto topico Combinatorics
ISBN 3-030-37853-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Folding Words Around Trees: Models Inspired by RNA -- Phylogenic Networks -- Tropical Geometry -- Chip Firing Games and Critical Groups -- Counting Tilings by Taking Walks in a Graph -- Beyond Coins, Stamps, and Chicken McNuggets: an Invitation to Numerical Semigroups -- Lateral Movement in Undergraduate Research: Case Studies in Number Theory -- Projects in (t,r) Broadcast Domination -- Squigonometry: Trigonomtry in the p-norm -- Researching in Undergraduate Mathematics Education -- Possible Directions for Both Undergraduate Students and Faculty -- Undergraduate Research in Mathematical Epidemiology.
Record Nr. UNINA-9910483905903321
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui