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 361-380 of 471 results.
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ID:
190
Year: 2007
Name: Marc Chamberland
Institution: Grinnell College
Subject area(s): sequences, number theory, dynamics, fractals
Title of Talk: The Mean-Median Map
Abstract: Starting with a non-empty finite set S_n={x_1,\ldots,x_n} contained in R, generate the unique number x_{n+1} which satisfies the mean-median equation (x_1 + \cdots + x_n + x_{n+1}/(n+1) = median(S_n) . As usual, we define the median of the set S_n = {x_1,\ldots,x_n}, where x_1<= ... <= x_n, as median (S_n) = \left\{ x_{(n+1)/2}, n odd , \frac{x_{n/2} + x_{n/2+1}}{2}, n even . By applying the mean-median equation repeatedly to a set one generates an infinite sequence {x_k}_{k=1}^\infty. The dynamics of this map are surprising! Most maps tend to have either relatively simple dynamics or chaotic dynamics. While the mean-median map seems to be asymptotically constant, it seems very hard to predict. This talk will showcase the work done to date. This is joint work with Mario Martelli (Claremont McKenna College).
Year: 2007
Name: Marc Chamberland
Institution: Grinnell College
Subject area(s): sequences, number theory, dynamics, fractals
Title of Talk: The Mean-Median Map
Abstract: Starting with a non-empty finite set S_n={x_1,\ldots,x_n} contained in R, generate the unique number x_{n+1} which satisfies the mean-median equation (x_1 + \cdots + x_n + x_{n+1}/(n+1) = median(S_n) . As usual, we define the median of the set S_n = {x_1,\ldots,x_n}, where x_1<= ... <= x_n, as median (S_n) = \left\{ x_{(n+1)/2}, n odd , \frac{x_{n/2} + x_{n/2+1}}{2}, n even . By applying the mean-median equation repeatedly to a set one generates an infinite sequence {x_k}_{k=1}^\infty. The dynamics of this map are surprising! Most maps tend to have either relatively simple dynamics or chaotic dynamics. While the mean-median map seems to be asymptotically constant, it seems very hard to predict. This talk will showcase the work done to date. This is joint work with Mario Martelli (Claremont McKenna College).
ID:
189
Year: 2007
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory, Dynamical Systems
Title of Talk: Pseudo-Random Walks
Abstract: In a recent Monthly article, O'Bryant, Reznick and Serbinowska [ORS] have given some fascinating new insights into the behavior of \[ S_{N}(\alpha) := \sum_{n=1}^N (-1)^{[n\alpha]} \] where [x] is the integer part of x. Since the fractional part of n*\alpha for n=1,2,3,\dots behaves 'random-ish', one can make various guesses and apply classical methods like exponential sums to explore these hypotheses. Remarkably, the guesses are often wrong and the classical methods don't seem to work very well. Instead, [ORS] use continued fractions to obtain sharp and explicit upper and lower bounds for |S_{\alpha}(N)| in terms of \log N, and as a by-product get a way of evaluating S_{\alpha}(N) for large N with amazing efficiency.\\ We will explain that last part of their work. Then we will show how to use exponential sums with a twist that gives a lower bound for |S_{\alpha}(N)| - less explicit, but more general than what the methods from [ORS] give you. And if we omit tedious computations (which we will, and which are only long, not hard), the approach is as clear-cut and beautiful as that using exponential sums to the case of the fractional part of n*\alpha. Lit.: K.~O'Bryant, B.~Reznick, M.~Serbinowska: {\em Almost alternating sums}, Monthly vol.~113/8, pp. 673-688. Prerequisites: only complex exponentials e^{it}.
Year: 2007
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory, Dynamical Systems
Title of Talk: Pseudo-Random Walks
Abstract: In a recent Monthly article, O'Bryant, Reznick and Serbinowska [ORS] have given some fascinating new insights into the behavior of \[ S_{N}(\alpha) := \sum_{n=1}^N (-1)^{[n\alpha]} \] where [x] is the integer part of x. Since the fractional part of n*\alpha for n=1,2,3,\dots behaves 'random-ish', one can make various guesses and apply classical methods like exponential sums to explore these hypotheses. Remarkably, the guesses are often wrong and the classical methods don't seem to work very well. Instead, [ORS] use continued fractions to obtain sharp and explicit upper and lower bounds for |S_{\alpha}(N)| in terms of \log N, and as a by-product get a way of evaluating S_{\alpha}(N) for large N with amazing efficiency.\\ We will explain that last part of their work. Then we will show how to use exponential sums with a twist that gives a lower bound for |S_{\alpha}(N)| - less explicit, but more general than what the methods from [ORS] give you. And if we omit tedious computations (which we will, and which are only long, not hard), the approach is as clear-cut and beautiful as that using exponential sums to the case of the fractional part of n*\alpha. Lit.: K.~O'Bryant, B.~Reznick, M.~Serbinowska: {\em Almost alternating sums}, Monthly vol.~113/8, pp. 673-688. Prerequisites: only complex exponentials e^{it}.
ID:
188
Year: 2007
Name: Neil Martinsen-Burrell
Institution: Wartburg College
Subject area(s): applied math, dynamical systems
Title of Talk: Assimilating Drifter Trajectories using Gradient Descent
Abstract: In geophysics, we frequently try to couple dynamical models of physical systems such as the atmosphere or ocean with direct observations of those systems. In the atmosphere, with fixed observing stations, there are advanced techniques for Numerical Weather Prediction. In the ocean, observations are often made by objects that drift with the flow. This presents difficulties for conventional data assimilation methods. I will discuss one possible way to assimilate drifter trajectories into a very simple dynamical model.
Year: 2007
Name: Neil Martinsen-Burrell
Institution: Wartburg College
Subject area(s): applied math, dynamical systems
Title of Talk: Assimilating Drifter Trajectories using Gradient Descent
Abstract: In geophysics, we frequently try to couple dynamical models of physical systems such as the atmosphere or ocean with direct observations of those systems. In the atmosphere, with fixed observing stations, there are advanced techniques for Numerical Weather Prediction. In the ocean, observations are often made by objects that drift with the flow. This presents difficulties for conventional data assimilation methods. I will discuss one possible way to assimilate drifter trajectories into a very simple dynamical model.
ID:
187
Year: 2007
Name: Thomas Britton
Institution: Coe College
Subject area(s):
Title of Talk: Dots and Lines
Abstract:
Year: 2007
Name: Thomas Britton
Institution: Coe College
Subject area(s):
Title of Talk: Dots and Lines
Abstract:
ID:
186
Year: 2007
Name: David Romano
Institution: Grinnell College
Subject area(s): Convex geometry
Title of Talk: Connected goalies for convex polygons
Abstract: Given a compact convex body K in the plane, call a connected 1-dimensional set G in the plane a goalie if it intersects all the straight lines that intersect K. This talk is concerned with the problem of finding the minimal length goalie for polygons. For any polygon P with n sides, we prove that any shortest goalie G for P has convex hull CH(G) a polygon with at most 2n sides. For triangles T, the minimal length goalie is the Steiner minimal tree for T. This is no longer true in the case of quadrilaterals, in which case a Steiner minimal tree need not be a minimal goalie.
Year: 2007
Name: David Romano
Institution: Grinnell College
Subject area(s): Convex geometry
Title of Talk: Connected goalies for convex polygons
Abstract: Given a compact convex body K in the plane, call a connected 1-dimensional set G in the plane a goalie if it intersects all the straight lines that intersect K. This talk is concerned with the problem of finding the minimal length goalie for polygons. For any polygon P with n sides, we prove that any shortest goalie G for P has convex hull CH(G) a polygon with at most 2n sides. For triangles T, the minimal length goalie is the Steiner minimal tree for T. This is no longer true in the case of quadrilaterals, in which case a Steiner minimal tree need not be a minimal goalie.
ID:
182
Year: 2007
Name: Jean Clipperton
Institution: Simpson College
Subject area(s): Graph Theory
Title of Talk: Strong Signals: L(d,2,1)-Labeling on Simple Graphs
Abstract: An L(d, 2, 1)-labeling is a simplified model for the channel assignment problem. It is a natural generalization of the widely studied L(2, 1) and L(3, 2, 1)-labeling. An L(d, 2, 1)-labeling of a graph G is a function f from the vertex set V(G) to the set of positive integers such that if the distance between vertices x and y is 1, then |f (x)- f (y)| >= d; if the distance between x and y is 2, then |f (x)- f(y)| >= 2; and if the distance between x and y is 3, then |f (x)- f (y)| >= 1. The L(d, 2, 1)-labeling number k_d(G) of G is the smallest positive integer k_d such that G has an L(d, 2, 1)-labeling with k_d as the maximum label. This talk will present general results for k_d when labeling simple graphs, such as paths, bipartite graphs, and cycles.
Year: 2007
Name: Jean Clipperton
Institution: Simpson College
Subject area(s): Graph Theory
Title of Talk: Strong Signals: L(d,2,1)-Labeling on Simple Graphs
Abstract: An L(d, 2, 1)-labeling is a simplified model for the channel assignment problem. It is a natural generalization of the widely studied L(2, 1) and L(3, 2, 1)-labeling. An L(d, 2, 1)-labeling of a graph G is a function f from the vertex set V(G) to the set of positive integers such that if the distance between vertices x and y is 1, then |f (x)- f (y)| >= d; if the distance between x and y is 2, then |f (x)- f(y)| >= 2; and if the distance between x and y is 3, then |f (x)- f (y)| >= 1. The L(d, 2, 1)-labeling number k_d(G) of G is the smallest positive integer k_d such that G has an L(d, 2, 1)-labeling with k_d as the maximum label. This talk will present general results for k_d when labeling simple graphs, such as paths, bipartite graphs, and cycles.
ID:
181
Year: 2007
Name: Charles Ashbacher
Institution: #none
Subject area(s):
Title of Talk: Computer Explorations of Prime Conjectures Made by Marnell
Abstract: In 1742, Goldbach made a conjecture that every even integer greater than 2 is expressible as the sum of two primes. While extensive computer searches have failed to find a counterexample, the general conjecture remains open, although nearly everyone believes that it is true. In a recent submission to Journal of Recreational Mathematics, Geoffrey Marnell made ten additional conjectures regarding what can be expressed using prime numbers. This paper gives the results of computer explorations carried out to test the conjectures.
Year: 2007
Name: Charles Ashbacher
Institution: #none
Subject area(s):
Title of Talk: Computer Explorations of Prime Conjectures Made by Marnell
Abstract: In 1742, Goldbach made a conjecture that every even integer greater than 2 is expressible as the sum of two primes. While extensive computer searches have failed to find a counterexample, the general conjecture remains open, although nearly everyone believes that it is true. In a recent submission to Journal of Recreational Mathematics, Geoffrey Marnell made ten additional conjectures regarding what can be expressed using prime numbers. This paper gives the results of computer explorations carried out to test the conjectures.
ID:
180
Year: 2007
Name: Wendy Weber
Institution: Central College
Subject area(s): teaching prospective teachers
Title of Talk: Mathematical Questions from the Classroom
Abstract: How can we bridge the gap between prospective teachers
Year: 2007
Name: Wendy Weber
Institution: Central College
Subject area(s): teaching prospective teachers
Title of Talk: Mathematical Questions from the Classroom
Abstract: How can we bridge the gap between prospective teachers
ID:
179
Year: 2007
Name: Russell Goodman
Institution: Central College
Subject area(s): Pedagogy; Elementary Mathematics
Title of Talk: Using Oral Exams to Help Prepare Future Elementary Mathematics Teachers
Abstract: The ability to effectively communicate mathematics is a priority for future elementary mathematics teachers. An oral examination, if used appropriately, is an excellent tool for assessing such skills. Moreover, an oral exam is a useful pedagogical tool for helping future elementary mathematics teachers improve their skills in communicating mathematical concepts. <br><br> The speaker has used oral exams in his department
Year: 2007
Name: Russell Goodman
Institution: Central College
Subject area(s): Pedagogy; Elementary Mathematics
Title of Talk: Using Oral Exams to Help Prepare Future Elementary Mathematics Teachers
Abstract: The ability to effectively communicate mathematics is a priority for future elementary mathematics teachers. An oral examination, if used appropriately, is an excellent tool for assessing such skills. Moreover, an oral exam is a useful pedagogical tool for helping future elementary mathematics teachers improve their skills in communicating mathematical concepts. <br><br> The speaker has used oral exams in his department
ID:
177
Year: 2006
Name: Kenneth Driessel
Institution: #non-IA section
Subject area(s): classical mechanics, bio-mechanics
Title of Talk: The Dynamics of a Planar Two Link Chain and Some Applications to Human Motion
Abstract: Try the following 'acceleration experiment': Stand balanced with your legs straight and a slight forward bend at the waist. Then step backwards. Consider the following 'acceleration question': How do humans initiate this motion? Or more generally: How do humans usually initiate horizontal motion from a balanced position? (I first met this question when thinking about cross country skiing.) We analyze the acceleration question by analogy. In particular, we study the classical dynamics of a mechanical system consisting of two linked rods. We assume that the first rod is connected to the ground by a hinge. (The first rod corresponds to the human legs. The ground hinge corresponds to the human ankles.) We assume that the second rod is connected to the first one by another hinge. (The second rod corresponds to the human torso. The second hinge corresponds to the human hips.) We derive the equations of motion for this mechanical system. We prove that if the system is initially at rest in a balanced position then gravity causes the center of mass to accelerate in the horizontal direction toward which the system is 'pointed'. We infer that the step backwards in the acceleration experiment is initiated by a relaxation of the muscles at the hips. Reference: Kenneth R. Driessel and Irvin R. Hentzel, 'Dynamics of a Planar Two Link Chain', http://www.fiberpipe.net/~driessel/2-links.pdf
Year: 2006
Name: Kenneth Driessel
Institution: #non-IA section
Subject area(s): classical mechanics, bio-mechanics
Title of Talk: The Dynamics of a Planar Two Link Chain and Some Applications to Human Motion
Abstract: Try the following 'acceleration experiment': Stand balanced with your legs straight and a slight forward bend at the waist. Then step backwards. Consider the following 'acceleration question': How do humans initiate this motion? Or more generally: How do humans usually initiate horizontal motion from a balanced position? (I first met this question when thinking about cross country skiing.) We analyze the acceleration question by analogy. In particular, we study the classical dynamics of a mechanical system consisting of two linked rods. We assume that the first rod is connected to the ground by a hinge. (The first rod corresponds to the human legs. The ground hinge corresponds to the human ankles.) We assume that the second rod is connected to the first one by another hinge. (The second rod corresponds to the human torso. The second hinge corresponds to the human hips.) We derive the equations of motion for this mechanical system. We prove that if the system is initially at rest in a balanced position then gravity causes the center of mass to accelerate in the horizontal direction toward which the system is 'pointed'. We infer that the step backwards in the acceleration experiment is initiated by a relaxation of the muscles at the hips. Reference: Kenneth R. Driessel and Irvin R. Hentzel, 'Dynamics of a Planar Two Link Chain', http://www.fiberpipe.net/~driessel/2-links.pdf
ID:
176
Year: 2006
Name: Jim Tattersall
Institution: Providence College
Subject area(s): History of Mathematics
Title of Talk: Vignettes in Number Theory
Abstract: Properties and the history of several numbers that lend themselves naturally to undergraduate research projects will be discussed. Topics include Demlo numbers, polite numbers, sad numbers, decimal Columbian numbers, Smith numbers, and Niven numbers.
Year: 2006
Name: Jim Tattersall
Institution: Providence College
Subject area(s): History of Mathematics
Title of Talk: Vignettes in Number Theory
Abstract: Properties and the history of several numbers that lend themselves naturally to undergraduate research projects will be discussed. Topics include Demlo numbers, polite numbers, sad numbers, decimal Columbian numbers, Smith numbers, and Niven numbers.
ID:
175
Year: 2006
Name: Jim Tattersall
Institution: Providence College
Subject area(s): History of Mathematics
Title of Talk: Episodes in The Early History of The Lucasian Chair
Abstract: In 1663, Henry Lucas, the long-time secretary to the Chancellor of the University of Cambridge, made a bequest, subsequently granted by Charles II, to endow a chair in mathematics. A number of conditions were attached to the Chair. Among the more prominent Lucasian professors were Newton, Babbage, Stokes, Dirac, and Hawking. We focus attention on the early Lucasians. Many of whom were very diligent in carrying out their Lucasian responsibilities but as history has shown such was not always the case. In the process, we uncover several untold stories and some interesting mathematics
Year: 2006
Name: Jim Tattersall
Institution: Providence College
Subject area(s): History of Mathematics
Title of Talk: Episodes in The Early History of The Lucasian Chair
Abstract: In 1663, Henry Lucas, the long-time secretary to the Chancellor of the University of Cambridge, made a bequest, subsequently granted by Charles II, to endow a chair in mathematics. A number of conditions were attached to the Chair. Among the more prominent Lucasian professors were Newton, Babbage, Stokes, Dirac, and Hawking. We focus attention on the early Lucasians. Many of whom were very diligent in carrying out their Lucasian responsibilities but as history has shown such was not always the case. In the process, we uncover several untold stories and some interesting mathematics
ID:
174
Year: 2006
Name: Ryan Martin
Institution: Iowa State University
Subject area(s): Graph Theory
Title of Talk: Vertex identifying codes in graphs: definitions, theorems and open problems
Abstract: In 1998, Karpovsky, Chakrabarty and Levitin introduced a new graph invariant called the vertex identification code. If C is a subset of the vertices, then C is a vertex-identifying code if each set N[v]\cap C is distinct and nonempty, where N[v] denotes the closed neighborhood of vertex v. We will discuss a number of results on the size of the smallest code in a graph, particularly on the Erdos-Renyi random graph and we will present open problems.
Year: 2006
Name: Ryan Martin
Institution: Iowa State University
Subject area(s): Graph Theory
Title of Talk: Vertex identifying codes in graphs: definitions, theorems and open problems
Abstract: In 1998, Karpovsky, Chakrabarty and Levitin introduced a new graph invariant called the vertex identification code. If C is a subset of the vertices, then C is a vertex-identifying code if each set N[v]\cap C is distinct and nonempty, where N[v] denotes the closed neighborhood of vertex v. We will discuss a number of results on the size of the smallest code in a graph, particularly on the Erdos-Renyi random graph and we will present open problems.
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:
172
Year: 2006
Name: Mariah Birgen
Institution: Wartburg College
Subject area(s): Linear Algebra, Voting Theory
Title of Talk: Decomposing Voters
Abstract: Recent developments in the mathematics of Social Choice by Don Saari, among others, have added an element of geometry and linear algebra to a field that has been dominated by combinatorics. This talk will introduce the linear algebra behind a three-candidate election, including how symmetries underlie traditional voting paradoxes.
Year: 2006
Name: Mariah Birgen
Institution: Wartburg College
Subject area(s): Linear Algebra, Voting Theory
Title of Talk: Decomposing Voters
Abstract: Recent developments in the mathematics of Social Choice by Don Saari, among others, have added an element of geometry and linear algebra to a field that has been dominated by combinatorics. This talk will introduce the linear algebra behind a three-candidate election, including how symmetries underlie traditional voting paradoxes.
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:
170
Year: 2006
Name: Alexander Kleiner
Institution: Drake University
Subject area(s): analysis, history of mathematics
Title of Talk: The Toeplitz-Silverman Theorem Part II
Abstract: In the first two decades of the twentieth century summability developed from collection of special results used in other parts of analysis into a full-blown field. One of the main points of this transition was a collection of general results that gave conditions for a method to sum every convergent sequence. Part I of this presentation, which was given last spring, laid out the work that led to the general theory. Papers by Toeplitz, Silverman, Kojima, Schur and others established the theory. This note will look at the development of these conditions and, as time permits, the reoccurrence of these results in the early day of the "Polish" school of functional analysis
Year: 2006
Name: Alexander Kleiner
Institution: Drake University
Subject area(s): analysis, history of mathematics
Title of Talk: The Toeplitz-Silverman Theorem Part II
Abstract: In the first two decades of the twentieth century summability developed from collection of special results used in other parts of analysis into a full-blown field. One of the main points of this transition was a collection of general results that gave conditions for a method to sum every convergent sequence. Part I of this presentation, which was given last spring, laid out the work that led to the general theory. Papers by Toeplitz, Silverman, Kojima, Schur and others established the theory. This note will look at the development of these conditions and, as time permits, the reoccurrence of these results in the early day of the "Polish" school of functional analysis
ID:
169
Year: 2006
Name: Rick Spellerberg
Institution: Simpson College
Subject area(s): Biology / Mathematics
Title of Talk: Sperm Competition Games
Abstract: Sperm Competition occurs when ejaculates of multiple males compete to fertilize the eggs of one female. In this talk we will discuss the work of G.A. Parker in his paper; Sperm Competition: sneaks and extra-pair copulations. In this paper, Parker examines ejaculation strategies for cases when an opportunist male "steals" a mating with the female of a paired male.
Year: 2006
Name: Rick Spellerberg
Institution: Simpson College
Subject area(s): Biology / Mathematics
Title of Talk: Sperm Competition Games
Abstract: Sperm Competition occurs when ejaculates of multiple males compete to fertilize the eggs of one female. In this talk we will discuss the work of G.A. Parker in his paper; Sperm Competition: sneaks and extra-pair copulations. In this paper, Parker examines ejaculation strategies for cases when an opportunist male "steals" a mating with the female of a paired male.
ID:
168
Year: 2006
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number theory, analytic
Title of Talk: Primitive prime divisors of Mersenne numbers via Uniform Distribution
Abstract: Given a sequence a of integers, a primitive divisor of a(n) is an integer which divides a(n) but no earlier term of the sequence. Last year, we presented a result about a weighted average of primitive prime divisors of the well-known Mersenne numbers M(n) = 2^n-1. This year, we have an entirely different, simple proof of the same result, using cyclotomic polynomials and uniform distribution. We are indebted to Carl Pomerance for helpful insights. We will also mention possible applications to other sequences like the Fibonacci numbers.
Year: 2006
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number theory, analytic
Title of Talk: Primitive prime divisors of Mersenne numbers via Uniform Distribution
Abstract: Given a sequence a of integers, a primitive divisor of a(n) is an integer which divides a(n) but no earlier term of the sequence. Last year, we presented a result about a weighted average of primitive prime divisors of the well-known Mersenne numbers M(n) = 2^n-1. This year, we have an entirely different, simple proof of the same result, using cyclotomic polynomials and uniform distribution. We are indebted to Carl Pomerance for helpful insights. We will also mention possible applications to other sequences like the Fibonacci numbers.
ID:
167
Year: 2006
Name: Marc Chamberland
Institution: Grinnell College
Subject area(s): undergrad level analysis
Title of Talk: Mathematics by Experiment
Abstract: The use of computer packages has brought us to a point where the computer can be used for many tasks: discover new mathematical patterns and relationships, create impressive graphics to expose mathematical structure, falsify conjectures, confirm analytically derived results, and perhaps most impressively for the purist, suggest approaches for formal proofs. This is the thrust of experimental mathematics. This talk will give some examples to discover or prove results concerning goemetry, integrals, binomial sums, and infinite series.
Year: 2006
Name: Marc Chamberland
Institution: Grinnell College
Subject area(s): undergrad level analysis
Title of Talk: Mathematics by Experiment
Abstract: The use of computer packages has brought us to a point where the computer can be used for many tasks: discover new mathematical patterns and relationships, create impressive graphics to expose mathematical structure, falsify conjectures, confirm analytically derived results, and perhaps most impressively for the purist, suggest approaches for formal proofs. This is the thrust of experimental mathematics. This talk will give some examples to discover or prove results concerning goemetry, integrals, binomial sums, and infinite series.