Proposals
Below are some proposals for talks from the past (and current). By clicking on the ID number, more details are shown. By default, these are sorted chronologically (recent first) and by then by last name. The data can be sorted by alternate means by using the links at the top right, each allowing ascending or descending orders.
Displaying 181-200 of 471 results.
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ID:
353
Year: 2013
Name: Jennifer Quinn
Institution: Mathematical Association of America
Subject area(s):
Title of Talk: Fibonacci's Flower Garden
Abstract: It has often been said that the Fibonacci numbers frequently occur in art, architecture, music, magic, and nature. This interactive investigation looks for evidence of this claim in the spiral patterns of plants. Is it synchronicity or divine intervention? Fate or dumb luck? We will explore a simple model to explain the occurrences and wonder whether other number sequences are equally likely to occur. This talk is designed to be appreciated by mathematicians and nonmathematicians alike. So join us in a mathematical adventure through Fibonacci's garden.
Year: 2013
Name: Jennifer Quinn
Institution: Mathematical Association of America
Subject area(s):
Title of Talk: Fibonacci's Flower Garden
Abstract: It has often been said that the Fibonacci numbers frequently occur in art, architecture, music, magic, and nature. This interactive investigation looks for evidence of this claim in the spiral patterns of plants. Is it synchronicity or divine intervention? Fate or dumb luck? We will explore a simple model to explain the occurrences and wonder whether other number sequences are equally likely to occur. This talk is designed to be appreciated by mathematicians and nonmathematicians alike. So join us in a mathematical adventure through Fibonacci's garden.
ID:
354
Year: 2013
Name: Jennifer Quinn
Institution: Mathematical Association of America
Subject area(s):
Title of Talk: Mathematics to DIE for: The Battle Between Counting and Matching
Abstract: Positive sums count. Alternating sums match. So which is "easier" to consider mathematically? From the analysis of infinite series, we know that if a positive sum converges, then its alternating sum must also converge but the converse is not true. From linear algebra, we know that the permanent of an n x n matrix is usually hard to calculate, whereas its alternating sum, the determinant, can be computed efficiently and it has many nice theoretical properties. This talk is one part performance art and three parts combinatorics. The audience will judge a combinatorial competition between the competing techniques. Be prepared to explore a variety of positive and alternating sums involving binomial coefficients, Fibonacci numbers, and other beautiful combinatorial quantities. How are the terms in each sum concretely interpreted? What is being counted? What is being matched? Do alternating sums always give simpler results? You decide.
Year: 2013
Name: Jennifer Quinn
Institution: Mathematical Association of America
Subject area(s):
Title of Talk: Mathematics to DIE for: The Battle Between Counting and Matching
Abstract: Positive sums count. Alternating sums match. So which is "easier" to consider mathematically? From the analysis of infinite series, we know that if a positive sum converges, then its alternating sum must also converge but the converse is not true. From linear algebra, we know that the permanent of an n x n matrix is usually hard to calculate, whereas its alternating sum, the determinant, can be computed efficiently and it has many nice theoretical properties. This talk is one part performance art and three parts combinatorics. The audience will judge a combinatorial competition between the competing techniques. Be prepared to explore a variety of positive and alternating sums involving binomial coefficients, Fibonacci numbers, and other beautiful combinatorial quantities. How are the terms in each sum concretely interpreted? What is being counted? What is being matched? Do alternating sums always give simpler results? You decide.
ID:
107
Year: 2005
Name: Scott Herriott
Institution: Maharishi University of Management
Subject area(s): Math education; college algebra
Title of Talk: The "Basic Four" Elementary Functions and Their Applications in College Algebra
Abstract: The "Basic Four" elementary functions are those that result from the association of an additive or multiplicative change in X with an additive or multiplicative change in Y (linear, exponential, logarithmic and power). We consider the importance of these functions in the college algebra course in terms of the breadth of their applications in the fields of study that college algebra students will major in.
Year: 2005
Name: Scott Herriott
Institution: Maharishi University of Management
Subject area(s): Math education; college algebra
Title of Talk: The "Basic Four" Elementary Functions and Their Applications in College Algebra
Abstract: The "Basic Four" elementary functions are those that result from the association of an additive or multiplicative change in X with an additive or multiplicative change in Y (linear, exponential, logarithmic and power). We consider the importance of these functions in the college algebra course in terms of the breadth of their applications in the fields of study that college algebra students will major in.
ID:
160
Year: 2006
Name: Catherine Gorini
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Visualizing Linear Algebra with Geometer
Abstract: I will present Sketchpad labs for visualizing the following concepts in linear algebra: Linear transformations and image, range, kernel, and projection. The determinant of a matrix and the orientation-preserving or-reversing property of the corresponding linear transformation. The determinant a matrix to the area of the image of a unit area under the corresponding linear transformation. Eigenvectors and eigenvalues
Year: 2006
Name: Catherine Gorini
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Visualizing Linear Algebra with Geometer
Abstract: I will present Sketchpad labs for visualizing the following concepts in linear algebra: Linear transformations and image, range, kernel, and projection. The determinant of a matrix and the orientation-preserving or-reversing property of the corresponding linear transformation. The determinant a matrix to the area of the image of a unit area under the corresponding linear transformation. Eigenvectors and eigenvalues
ID:
173
Year: 2006
Name: M. Anne Dow
Institution: Maharishi University of Management
Subject area(s): Developmental math course materials
Title of Talk: Some Hands-on Workshops for Elementary and Intermediate Algebra Courses
Abstract: I found all the topics of my Elementary and Intermediate Algebra courses in the greenhouses we recently built on campus to provide organic vegetables for our campus dining hall. In my talk I will present two workshops on linear functions, one about the amount of broccoli seed needed to produce N thousand pounds of broccoli per week, and one about heat loss to the greenhouse during winter. Both require students to think carefully about what the slope means.
Year: 2006
Name: M. Anne Dow
Institution: Maharishi University of Management
Subject area(s): Developmental math course materials
Title of Talk: Some Hands-on Workshops for Elementary and Intermediate Algebra Courses
Abstract: I found all the topics of my Elementary and Intermediate Algebra courses in the greenhouses we recently built on campus to provide organic vegetables for our campus dining hall. In my talk I will present two workshops on linear functions, one about the amount of broccoli seed needed to produce N thousand pounds of broccoli per week, and one about heat loss to the greenhouse during winter. Both require students to think carefully about what the slope means.
ID:
206
Year: 2007
Name: M Anne Dow
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Mathematics for Sustainable Living: Pre-Calculus Basics
Abstract: This talk describes a new math course I am designing for our Sustainable Living students. The purpose of the Sustainable Living major is to equip students to design, build, and maintain sustainable communities. The prerequisite for the new math course is Intermediate Algebra. It will cover simple linear models, exponential and logarithmic functions, graphs of functions, trigonometry of triangles, and elementary probability, all in the context of problems and topics arising in our Sustainable Living major.
Year: 2007
Name: M Anne Dow
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Mathematics for Sustainable Living: Pre-Calculus Basics
Abstract: This talk describes a new math course I am designing for our Sustainable Living students. The purpose of the Sustainable Living major is to equip students to design, build, and maintain sustainable communities. The prerequisite for the new math course is Intermediate Algebra. It will cover simple linear models, exponential and logarithmic functions, graphs of functions, trigonometry of triangles, and elementary probability, all in the context of problems and topics arising in our Sustainable Living major.
ID:
207
Year: 2007
Name: Catherine Gorini
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Geometry for the Artist: A General Education Course
Abstract: This paper will describe the course Geometry for the Artist that I have been teaching for over 20 years at M.U.M. The topics covered symmetry, Euclidean geometry, perspective, fractals, non-Euclidean geometry, and topology. For each topic, we discuss applications in the visual arts with an emphasis on M. C. Escher. This course satisfies the distribution requirement for mathematics.
Year: 2007
Name: Catherine Gorini
Institution: Maharishi University of Management
Subject area(s):
Title of Talk: Geometry for the Artist: A General Education Course
Abstract: This paper will describe the course Geometry for the Artist that I have been teaching for over 20 years at M.U.M. The topics covered symmetry, Euclidean geometry, perspective, fractals, non-Euclidean geometry, and topology. For each topic, we discuss applications in the visual arts with an emphasis on M. C. Escher. This course satisfies the distribution requirement for mathematics.
ID:
136
Year: 2005
Name: David Bressoud
Institution: Macalester College
Subject area(s): Mathematics Curriculum
Title of Talk: Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004
Abstract: The MAA's Committee on the Undergraduate Program in Mathematics (CUPM) is charged with making recommendations to guide mathematics departments in designing curricula for their undergraduate students. The CUPM Curriculum Guide 2004, published last Fall provides an up-to-date perspective on the mathematics curriculum for many different student audiences, including of course our own majors. This session will be a presentation followed by a question and answer session with committee member David Bressoud from Macalester College. Free copies of the Guide and Curriculum Foundations Project will be available for those who come to the session.
Year: 2005
Name: David Bressoud
Institution: Macalester College
Subject area(s): Mathematics Curriculum
Title of Talk: Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004
Abstract: The MAA's Committee on the Undergraduate Program in Mathematics (CUPM) is charged with making recommendations to guide mathematics departments in designing curricula for their undergraduate students. The CUPM Curriculum Guide 2004, published last Fall provides an up-to-date perspective on the mathematics curriculum for many different student audiences, including of course our own majors. This session will be a presentation followed by a question and answer session with committee member David Bressoud from Macalester College. Free copies of the Guide and Curriculum Foundations Project will be available for those who come to the session.
ID:
345
Year: 2012
Name: Ivars Peterson
Institution: MAA
Subject area(s): Mathematical Art & Geometry
Title of Talk: Geometreks
Abstract: Few people expect to encounter mathematics on a visit to an art gallery or even a walk down a city street (or across campus). When we explore the world around us with mathematics in mind, however, we see the many ways in which mathematics can manifest itself, in streetscapes, sculptures, paintings, architectural structures, and more. This illustrated presentation offers illuminating glimpses of mathematics, from Euclidean geometry and normal distributions to Riemann sums and M_bius strips, as seen in a variety of structures and artworks in Washington, D.C., Philadelphia, Toronto, Ottawa, Montreal, New Orleans, and many other locales.
Year: 2012
Name: Ivars Peterson
Institution: MAA
Subject area(s): Mathematical Art & Geometry
Title of Talk: Geometreks
Abstract: Few people expect to encounter mathematics on a visit to an art gallery or even a walk down a city street (or across campus). When we explore the world around us with mathematics in mind, however, we see the many ways in which mathematics can manifest itself, in streetscapes, sculptures, paintings, architectural structures, and more. This illustrated presentation offers illuminating glimpses of mathematics, from Euclidean geometry and normal distributions to Riemann sums and M_bius strips, as seen in a variety of structures and artworks in Washington, D.C., Philadelphia, Toronto, Ottawa, Montreal, New Orleans, and many other locales.
ID:
346
Year: 2012
Name: Ivars Peterson
Institution: MAA
Subject area(s): Mathematical Counting
Title of Talk: Pancake Sorting, Prefix Reversals, and DNA Rearrangements
Abstract: The seemingly simple problem of sorting a stack of differently sized pancakes has become a staple of theoretical computer science and led to insights into the evolution of species. First proposed in The American Mathematical Monthly, the problem attracted the attention of noted mathematicians and computer scientists. It now plays an important role in the realm of molecular biology for making sense of DNA rearrangements.
Year: 2012
Name: Ivars Peterson
Institution: MAA
Subject area(s): Mathematical Counting
Title of Talk: Pancake Sorting, Prefix Reversals, and DNA Rearrangements
Abstract: The seemingly simple problem of sorting a stack of differently sized pancakes has become a staple of theoretical computer science and led to insights into the evolution of species. First proposed in The American Mathematical Monthly, the problem attracted the attention of noted mathematicians and computer scientists. It now plays an important role in the realm of molecular biology for making sense of DNA rearrangements.
ID:
289
Year: 2010
Name: Ruth Berger
Institution: Luther College
Subject area(s): Algebra, Group Theory
Title of Talk: Exploring Group Theory with FGB
Abstract: Finite Group Behavior (FGB) is a free windows-based program that gives beginning group theory students a chance to explore abstract group theory concepts in a very concrete setting. The heart of the software is an extensive collection of Cayley tables of groups: Cyclic groups, Dihedral groups, and groups whose structure is not immediately recognizable. Students can explore relations among the elements of a group, determine the order of each element, and even make subgroups generated by selected elements of the group. This easy to use program also includes features that allow for the investigation of isomorphisms of groups, and it gives a nice visualization of how Cosets are formed. I will share some of the worksheets that I wrote for my Abstract Algebra students to gain some hands-on experience with these otherwise abstract concepts.
Year: 2010
Name: Ruth Berger
Institution: Luther College
Subject area(s): Algebra, Group Theory
Title of Talk: Exploring Group Theory with FGB
Abstract: Finite Group Behavior (FGB) is a free windows-based program that gives beginning group theory students a chance to explore abstract group theory concepts in a very concrete setting. The heart of the software is an extensive collection of Cayley tables of groups: Cyclic groups, Dihedral groups, and groups whose structure is not immediately recognizable. Students can explore relations among the elements of a group, determine the order of each element, and even make subgroups generated by selected elements of the group. This easy to use program also includes features that allow for the investigation of isomorphisms of groups, and it gives a nice visualization of how Cosets are formed. I will share some of the worksheets that I wrote for my Abstract Algebra students to gain some hands-on experience with these otherwise abstract concepts.
ID:
52
Year: 2004
Name: Ruth Berger
Institution: Luther College
Subject area(s): algebra
Title of Talk: Fun & Games with Permutation groups
Abstract: This talk will give an introduction to the
Year: 2004
Name: Ruth Berger
Institution: Luther College
Subject area(s): algebra
Title of Talk: Fun & Games with Permutation groups
Abstract: This talk will give an introduction to the
ID:
310
Year: 2011
Name: Ruth Berger
Institution: Luther College
Subject area(s): Calculus (special session 1)
Title of Talk: Calculus at Luther College
Abstract: Calculus at Luther College: Over the past two decades Calculus instruction at Luther has slowly moved from Reform Calculus back towards a more traditional approach. Several aspects of Reform Calculus, especially the use of technology, have been retained as essential components to teaching Calculus in the modern age. The main reason we moved back to a more traditional way of teaching Calculus was that we found we needed a more intellectually challenging course with sound theoretical foundations for our math majors.
Year: 2011
Name: Ruth Berger
Institution: Luther College
Subject area(s): Calculus (special session 1)
Title of Talk: Calculus at Luther College
Abstract: Calculus at Luther College: Over the past two decades Calculus instruction at Luther has slowly moved from Reform Calculus back towards a more traditional approach. Several aspects of Reform Calculus, especially the use of technology, have been retained as essential components to teaching Calculus in the modern age. The main reason we moved back to a more traditional way of teaching Calculus was that we found we needed a more intellectually challenging course with sound theoretical foundations for our math majors.
ID:
333
Year: 2012
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: A line need not be straight!
Abstract: In Geometry a line is an undefined term, governed only by whatever axioms you want to impose on it. Students have a hard time with proofs in non-Euclidean Geometries, because their Euclidean intuition about straight lines keeps interfering with their logical thinking. I try to have my students develop non-Euclidean intuition by introducing them to different worlds: The Green Jello World, inhabited by fish, consists of Jello that is less dense in one direction, but infinitely dense at the end of the world. Escher's World is as a disk populated by inhabitants in which everything shrinks towards the outside. By thinking like inhabitants of these worlds, students realize that you can get from A to B with fewer steps/flipper strokes by not necessarily following a Euclidean line. They naturally come up with the fact that lines (interpreted as shortest paths) can be curved looking paths! Having this hyperbolic intuition makes it much easier for students to write formal proofs in hyperbolic geometry.
Year: 2012
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: A line need not be straight!
Abstract: In Geometry a line is an undefined term, governed only by whatever axioms you want to impose on it. Students have a hard time with proofs in non-Euclidean Geometries, because their Euclidean intuition about straight lines keeps interfering with their logical thinking. I try to have my students develop non-Euclidean intuition by introducing them to different worlds: The Green Jello World, inhabited by fish, consists of Jello that is less dense in one direction, but infinitely dense at the end of the world. Escher's World is as a disk populated by inhabitants in which everything shrinks towards the outside. By thinking like inhabitants of these worlds, students realize that you can get from A to B with fewer steps/flipper strokes by not necessarily following a Euclidean line. They naturally come up with the fact that lines (interpreted as shortest paths) can be curved looking paths! Having this hyperbolic intuition makes it much easier for students to write formal proofs in hyperbolic geometry.
ID:
367
Year: 2013
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: Taxicab Geometry
Abstract: Making a small change in how distance is measured has a huge effect on the geometry of the plane. Circles now look like squares, Pi is an integer, and many other familiar objects have very unfamiliar shapes. Tilting a segment changes its size! Working in this geometry reinforces important skills that every math major needs to have: carefully read definitions and not make any assumptions based on intuition or previous experience. In this talk I will present some of the findings that my geometry students are expected to come up with.
Year: 2013
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: Taxicab Geometry
Abstract: Making a small change in how distance is measured has a huge effect on the geometry of the plane. Circles now look like squares, Pi is an integer, and many other familiar objects have very unfamiliar shapes. Tilting a segment changes its size! Working in this geometry reinforces important skills that every math major needs to have: carefully read definitions and not make any assumptions based on intuition or previous experience. In this talk I will present some of the findings that my geometry students are expected to come up with.
ID:
123
Year: 2005
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: Escher's World and Green Jello World - A Concrete Introduction to Hyperbolic Geometry
Abstract: Understanding theorems in non-Euclidean Geometry can be challenging to people who live in a Euclidean World. Since we do live on a sphere, Elliptic geometry makes some sense, but Hyperbolic geometry completely defies all our intuition. I will present two concrete examples of Poincare's models, which in class I refer to as "Escher's World" and the "Green Jello World". Thinking about what the inhabitants of these worlds might consider to be a straight line and other geometric concepts lets students accept the fact that Hyperbolic geometry is in fact just as natural as Euclidean Geometry.
Year: 2005
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: Escher's World and Green Jello World - A Concrete Introduction to Hyperbolic Geometry
Abstract: Understanding theorems in non-Euclidean Geometry can be challenging to people who live in a Euclidean World. Since we do live on a sphere, Elliptic geometry makes some sense, but Hyperbolic geometry completely defies all our intuition. I will present two concrete examples of Poincare's models, which in class I refer to as "Escher's World" and the "Green Jello World". Thinking about what the inhabitants of these worlds might consider to be a straight line and other geometric concepts lets students accept the fact that Hyperbolic geometry is in fact just as natural as Euclidean Geometry.
ID:
405
Year: 2014
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: Conic Sections in Grid City
Abstract: I will present some word problems that can be used at the high school level, or with pre-service teachers, to make students think about the definition of distance and the definitions of the figures known as conic sections in Euclidean Geometry. These real-world problems about distance measurement on a city grid introduce students to Taxicab geometry, an easily accessible topic that can lead to thought provoking questions at many different levels.
Year: 2014
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: Conic Sections in Grid City
Abstract: I will present some word problems that can be used at the high school level, or with pre-service teachers, to make students think about the definition of distance and the definitions of the figures known as conic sections in Euclidean Geometry. These real-world problems about distance measurement on a city grid introduce students to Taxicab geometry, an easily accessible topic that can lead to thought provoking questions at many different levels.
ID:
406
Year: 2014
Name: Mike Johnson
Institution: Luther College
Subject area(s):
Title of Talk: Missing Avalanche Sizes in the 1 dimensional sandpile model
Abstract: The one-dimensional sandpile model has many interesting connections with number theory. When looking at the size of sandpile avalanches, powers of 2 seem to be mysteriously absent. Using a trough model, we classify avalanches into two categories. The size of each type can be described as either a sum of consecutive integers or a product of two integers with controlled sum. Since powers of two cannot be written as a sum of two or more consecutive positive integers, this explains why powers of two are not common avalanche sizes. We then estimate the minimal sandpile length required to find an avalanche of a given size.
Year: 2014
Name: Mike Johnson
Institution: Luther College
Subject area(s):
Title of Talk: Missing Avalanche Sizes in the 1 dimensional sandpile model
Abstract: The one-dimensional sandpile model has many interesting connections with number theory. When looking at the size of sandpile avalanches, powers of 2 seem to be mysteriously absent. Using a trough model, we classify avalanches into two categories. The size of each type can be described as either a sum of consecutive integers or a product of two integers with controlled sum. Since powers of two cannot be written as a sum of two or more consecutive positive integers, this explains why powers of two are not common avalanche sizes. We then estimate the minimal sandpile length required to find an avalanche of a given size.
ID:
171
Year: 2006
Name: Reginald Laursen
Institution: Luther College
Subject area(s): Real Analysis
Title of Talk: Classroom Capsule: Teaching Challenge-Response Arguments
Abstract: The forward-backward method is a fundamental proof technique for helping students understand how to construct proofs. I will describe my latest variation in the application of this technique for addressing challenge-response arguments in a Real Analysis class. Using this variation my lower ability students have had greater success.
Year: 2006
Name: Reginald Laursen
Institution: Luther College
Subject area(s): Real Analysis
Title of Talk: Classroom Capsule: Teaching Challenge-Response Arguments
Abstract: The forward-backward method is a fundamental proof technique for helping students understand how to construct proofs. I will describe my latest variation in the application of this technique for addressing challenge-response arguments in a Real Analysis class. Using this variation my lower ability students have had greater success.
ID:
446
Year: 2016
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: Geometry software: Cinderella
Abstract: Cinderella is an easy to use dynamic software program which allows for constructions in Euclidean, Hyperbolic, and Elliptic geometries. Hyperbolic geometry uses the Poincare disk model. The menu selection in Cinderella is similar to Geometer’s Sketchpad. My course focuses on proofs, but almost every week I have an exploratory Cinderella lab, so students can get a feeling for these other geometries and make conjectures. Well known Euclidean results are verified while students get used to the menu items needed in the construction, then they explore the same construction in the other geometries. In this talk sample questions will be presented and several lab activities will be demonstrated. Cinderella can be downloaded for free at Cinderella.de
Year: 2016
Name: Ruth Berger
Institution: Luther College
Subject area(s): Geometry
Title of Talk: Geometry software: Cinderella
Abstract: Cinderella is an easy to use dynamic software program which allows for constructions in Euclidean, Hyperbolic, and Elliptic geometries. Hyperbolic geometry uses the Poincare disk model. The menu selection in Cinderella is similar to Geometer’s Sketchpad. My course focuses on proofs, but almost every week I have an exploratory Cinderella lab, so students can get a feeling for these other geometries and make conjectures. Well known Euclidean results are verified while students get used to the menu items needed in the construction, then they explore the same construction in the other geometries. In this talk sample questions will be presented and several lab activities will be demonstrated. Cinderella can be downloaded for free at Cinderella.de