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 341-360 of 471 results.
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ID:
144
Year: 2006
Name: Dave L. Renfro
Institution: ACT Inc.
Subject area(s): transcendental equations
Title of Talk: The Remarkable Equation tan(x) = x
Abstract: Although tan(x) = x is virtually the prototypical example for solving an equation by graphical methods, and this equation frequently appears in calculus texts as an example of Newton's method, there seems to be nothing in the literature that surveys what is known about its solutions. In this talk I will look at some appearances of this equation in elementary calculus, some appearances of this equation in more advanced areas (quantum mechanics, heat conduction, etc.), the fact that this equation has no nonreal solutions and that all of its nonzero solutions are transcendental, and some curious infinite sums involving its solutions. In addition, I will discuss some of the history behind this equation, including contributions by Euler (1748), Fourier (1807), Cauchy (1827), and Rayleigh (1874, 1877).
Year: 2006
Name: Dave L. Renfro
Institution: ACT Inc.
Subject area(s): transcendental equations
Title of Talk: The Remarkable Equation tan(x) = x
Abstract: Although tan(x) = x is virtually the prototypical example for solving an equation by graphical methods, and this equation frequently appears in calculus texts as an example of Newton's method, there seems to be nothing in the literature that surveys what is known about its solutions. In this talk I will look at some appearances of this equation in elementary calculus, some appearances of this equation in more advanced areas (quantum mechanics, heat conduction, etc.), the fact that this equation has no nonreal solutions and that all of its nonzero solutions are transcendental, and some curious infinite sums involving its solutions. In addition, I will discuss some of the history behind this equation, including contributions by Euler (1748), Fourier (1807), Cauchy (1827), and Rayleigh (1874, 1877).
ID:
432
Year: 2015
Name: Dave Richeson
Institution: Dickinson College
Subject area(s):
Title of Talk: The Four Problems of Antiquity
Abstract: We discuss the history of four of the most famous problems in mathematics-the so-called problems of antiquity: squaring the circle, trisecting the angle, doubling the cube, and constructing regular n-gons. We know the outcome-that they are all impossible to solve using compass and straightedge. But there is a long and fascinating history of mathematicians' attempts to solve the problems using the Euclidean tools and their success at solving them by other means (using marked straightedges, conic sections, transcendental curves, and mechanical devices). Like all great mathematical problems, they pushed mathematics forward.
Year: 2015
Name: Dave Richeson
Institution: Dickinson College
Subject area(s):
Title of Talk: The Four Problems of Antiquity
Abstract: We discuss the history of four of the most famous problems in mathematics-the so-called problems of antiquity: squaring the circle, trisecting the angle, doubling the cube, and constructing regular n-gons. We know the outcome-that they are all impossible to solve using compass and straightedge. But there is a long and fascinating history of mathematicians' attempts to solve the problems using the Euclidean tools and their success at solving them by other means (using marked straightedges, conic sections, transcendental curves, and mechanical devices). Like all great mathematical problems, they pushed mathematics forward.
ID:
532
Year: 2019
Name: Michael Rieck
Institution: Drake University
Subject area(s): Elliptic curves, algebraic geometry, projective geometry
Title of Talk: Elliptic Curves and the Perspective 3-Point Problem
Abstract: The Perspective-Three-Point Problem (P3P), a camera tracking problem, is solved by first focusing on determining the directions of the lines through pairs of control points, relative to the camera, rather than the distances from the camera to the control points. The analysis of this produces an efficient, accurate and reasonably simple P3P solver, which has been compared with a state-of-the-art P3P solver. However, the principal value of the present work is not in introducing yet another P3P solver, but lies rather in the discovery of an intimate connection between the P3P problem and a special family of elliptic curves that includes curves utilized in cryptography. This holds the potential for further advances in a number of directions. To make this connection, an interesting spherical analogue of an ancient “sliding” problem is stated and solved.
Year: 2019
Name: Michael Rieck
Institution: Drake University
Subject area(s): Elliptic curves, algebraic geometry, projective geometry
Title of Talk: Elliptic Curves and the Perspective 3-Point Problem
Abstract: The Perspective-Three-Point Problem (P3P), a camera tracking problem, is solved by first focusing on determining the directions of the lines through pairs of control points, relative to the camera, rather than the distances from the camera to the control points. The analysis of this produces an efficient, accurate and reasonably simple P3P solver, which has been compared with a state-of-the-art P3P solver. However, the principal value of the present work is not in introducing yet another P3P solver, but lies rather in the discovery of an intimate connection between the P3P problem and a special family of elliptic curves that includes curves utilized in cryptography. This holds the potential for further advances in a number of directions. To make this connection, an interesting spherical analogue of an ancient “sliding” problem is stated and solved.
ID:
125
Year: 2005
Name: Michael Rieck
Institution: Drake University
Subject area(s): special functions
Title of Talk: A Multiple Integral of a Piecewise Algebraic Function.
Abstract: Fix r>0. Let (x_0, y_0) and (x_n, y_n) be fixed and a distance r apart. Consider the set of all points ( x_1, y_1, x_2, y_2,..., x_{n-1}, y_{n-1} ) in Euclidean (2n-2)-space for which the distance in the plane between (x_{j-1}, y_{j-1}) and (x_j, y_j) never exceeds one (j=1,...,n). The hyper-volume of this set of points in (2n-2)-space can clearly be expressed as a multiple integral, integrating over 2n-2 dimensions, a function that is 1 on the set, but 0 off of the set. Surprisingly, it can also be expressed as a multiple integral over n-1 dimensions, of a piece-wise algebraic function.
Year: 2005
Name: Michael Rieck
Institution: Drake University
Subject area(s): special functions
Title of Talk: A Multiple Integral of a Piecewise Algebraic Function.
Abstract: Fix r>0. Let (x_0, y_0) and (x_n, y_n) be fixed and a distance r apart. Consider the set of all points ( x_1, y_1, x_2, y_2,..., x_{n-1}, y_{n-1} ) in Euclidean (2n-2)-space for which the distance in the plane between (x_{j-1}, y_{j-1}) and (x_j, y_j) never exceeds one (j=1,...,n). The hyper-volume of this set of points in (2n-2)-space can clearly be expressed as a multiple integral, integrating over 2n-2 dimensions, a function that is 1 on the set, but 0 off of the set. Surprisingly, it can also be expressed as a multiple integral over n-1 dimensions, of a piece-wise algebraic function.
ID:
555
Year: 2019
Name: Matt Rissler
Institution: Loras College
Subject area(s):
Title of Talk: The Math of Data Science
Abstract: Data Science is one of the buzzwordiest fields right now. In this talk, I will try to define Data Science out of my work implementing it as an undergraduate major at Loras. Then I will go on to talk about where Mathematics, both from the undergraduate and graduate curricula, is integral to the development and perhaps practice of Data Science.
Year: 2019
Name: Matt Rissler
Institution: Loras College
Subject area(s):
Title of Talk: The Math of Data Science
Abstract: Data Science is one of the buzzwordiest fields right now. In this talk, I will try to define Data Science out of my work implementing it as an undergraduate major at Loras. Then I will go on to talk about where Mathematics, both from the undergraduate and graduate curricula, is integral to the development and perhaps practice of Data Science.
ID:
302
Year: 2010
Name: Matthew Rissler
Institution: Loras College
Subject area(s):
Title of Talk: Starting a Math Colloquium: Experiences from Loras College
Abstract: Also presenting: Angela Kohlhass (Loras College). In this talk, the speakers will describe their experiences initiating and maintaining the Loras College half of the Bi-State Mathematics Colloquium. The BSMC is a partnership between the math departments of UW-Platteville and Loras College and is in its second year. The Loras talks provide a venue for Loras math students and faculty to hear from mathematicians in the region surrounding Loras College on a biweekly basis. Topics that will be addressed in this talk include finding speakers, getting students to attend, establishing regional buy-in, and the issues that we have yet to resolve.
Year: 2010
Name: Matthew Rissler
Institution: Loras College
Subject area(s):
Title of Talk: Starting a Math Colloquium: Experiences from Loras College
Abstract: Also presenting: Angela Kohlhass (Loras College). In this talk, the speakers will describe their experiences initiating and maintaining the Loras College half of the Bi-State Mathematics Colloquium. The BSMC is a partnership between the math departments of UW-Platteville and Loras College and is in its second year. The Loras talks provide a venue for Loras math students and faculty to hear from mathematicians in the region surrounding Loras College on a biweekly basis. Topics that will be addressed in this talk include finding speakers, getting students to attend, establishing regional buy-in, and the issues that we have yet to resolve.
ID:
328
Year: 2012
Name: Matt Rissler
Institution: Loras College
Subject area(s): Introductory Stats, Teaching with Technology
Title of Talk: Writing WeBWorK questions for Introductory Statistics
Abstract: WeBWorK is an Open-Source online homework system for Mathematics. The Open Problem Library contains many usable questions for Introductory Statistics. In this talk, I will discuss the current procedures for writing questions for Statistics and what improvements I have accomplished to simplify writing questions.
Year: 2012
Name: Matt Rissler
Institution: Loras College
Subject area(s): Introductory Stats, Teaching with Technology
Title of Talk: Writing WeBWorK questions for Introductory Statistics
Abstract: WeBWorK is an Open-Source online homework system for Mathematics. The Open Problem Library contains many usable questions for Introductory Statistics. In this talk, I will discuss the current procedures for writing questions for Statistics and what improvements I have accomplished to simplify writing questions.
ID:
374
Year: 2013
Name: Matt Rissler
Institution: Loras College
Subject area(s): Teaching
Title of Talk: Using Smartpens to Aid Student Learning
Abstract: Smartpens store writing and audio in a digital format that can be converted into various formats. In this talk, I will be discussing how I have used a smartpen to provide students with a variety of aids for learning Mathematics. All with relatively low overhead for the instructor.
Year: 2013
Name: Matt Rissler
Institution: Loras College
Subject area(s): Teaching
Title of Talk: Using Smartpens to Aid Student Learning
Abstract: Smartpens store writing and audio in a digital format that can be converted into various formats. In this talk, I will be discussing how I have used a smartpen to provide students with a variety of aids for learning Mathematics. All with relatively low overhead for the instructor.
ID:
408
Year: 2014
Name: Matt Rissler
Institution: Loras College
Subject area(s):
Title of Talk: Adding Context to Calculus
Abstract: This semester in Calculus I, my students have been doing weekly assignments to help provide them with context for the mathematics they are learning in the rest of the course. These assignments have investigated connections to historical and present day developments in mathematics, as well as to the utility of calculus for problem-solving in students' current lives and future careers. I will discuss what assignments I have done/will do and how students have responded to them.
Year: 2014
Name: Matt Rissler
Institution: Loras College
Subject area(s):
Title of Talk: Adding Context to Calculus
Abstract: This semester in Calculus I, my students have been doing weekly assignments to help provide them with context for the mathematics they are learning in the rest of the course. These assignments have investigated connections to historical and present day developments in mathematics, as well as to the utility of calculus for problem-solving in students' current lives and future careers. I will discuss what assignments I have done/will do and how students have responded to them.
ID:
423
Year: 2015
Name: Matt Rissler
Institution: Loras College
Subject area(s): Sports Analytics
Title of Talk: Another College Football Ranking
Abstract: Anyone who has followed D1A college football in the last two decades is aware that there computer rankings and probably has opinions on them. In this talk we will discuss my ranking which is a tweak of the Colley Matrix method, one of the former BCS rankings. My ranking uses a little bit of discrete probability, linear algebra, graph theory, and stochastic systems to arrive at its results.
Year: 2015
Name: Matt Rissler
Institution: Loras College
Subject area(s): Sports Analytics
Title of Talk: Another College Football Ranking
Abstract: Anyone who has followed D1A college football in the last two decades is aware that there computer rankings and probably has opinions on them. In this talk we will discuss my ranking which is a tweak of the Colley Matrix method, one of the former BCS rankings. My ranking uses a little bit of discrete probability, linear algebra, graph theory, and stochastic systems to arrive at its results.
ID:
461
Year: 2016
Name: Matt Rissler
Institution: Loras College
Subject area(s):
Title of Talk: Sports Analytics in Lower Level Courses
Abstract: I'll provide examples from baseball and basketball of sports analytics problems I have done in lower level classes, from College Algebra to Calculus II.
Year: 2016
Name: Matt Rissler
Institution: Loras College
Subject area(s):
Title of Talk: Sports Analytics in Lower Level Courses
Abstract: I'll provide examples from baseball and basketball of sports analytics problems I have done in lower level classes, from College Algebra to Calculus II.
ID:
483
Year: 2017
Name: Matt Rissler
Institution: Loras College
Subject area(s): Linear Algebra, Sports Analytics, Computing
Title of Talk: Ranking teams, predicting outcomes, tuning parameters and getting stuck
Abstract: I have been ranking sports for the last couple years, using a combination of a Markov Chain for determining the quality of a win based on the margin of victory, and a Markov Chain for aggregating results across the network of games. From this information, I've started predicting the outcome of games, however, this raises an interesting eigenvector problem that I have yet to solve. In this talk, I'll describe my rankings, give some rankings/predictions, describe the problems I've run into, and describe the future plans for improving my rankings.
Year: 2017
Name: Matt Rissler
Institution: Loras College
Subject area(s): Linear Algebra, Sports Analytics, Computing
Title of Talk: Ranking teams, predicting outcomes, tuning parameters and getting stuck
Abstract: I have been ranking sports for the last couple years, using a combination of a Markov Chain for determining the quality of a win based on the margin of victory, and a Markov Chain for aggregating results across the network of games. From this information, I've started predicting the outcome of games, however, this raises an interesting eigenvector problem that I have yet to solve. In this talk, I'll describe my rankings, give some rankings/predictions, describe the problems I've run into, and describe the future plans for improving my rankings.
ID:
522
Year: 2018
Name: Lorenzo Riva
Institution: Creighton University
Subject area(s):
Title of Talk: Feynman Operational Calculus
Abstract: The forthcoming paper "Combining continuous and discrete phenomena for Feynman's operational calculus in the presence of a $(C_0)$ semigroup and Feynman-Kac formulas with Lebesgue-Stieltjes measures" (by L. Nielsen, to appear in Integral Equations and Operator Theory) contains, as its main result, an evolution equation which serves to describe how Feynman's operational calculus evolves with time in the presence of a $(C_0)$ semigroup of linear operators. There are several examples in this paper which give rise to so-called, Feynman-Kac formulas with Lebesgue- Stieltjes measures (first investigated from a function space integral point of view by M. L. Lapidus in the late 1980s). However, due to the different approach, the Feynman-Kac formulas obtained in the paper by Nielsen have some significant differences from those obtained by Lapidus. An associated operator differential equation (essentially a nonhomogeneous Schrodinger's equation) is also obtained in Nielsen's paper. This talk will concentrate on the explanation of the newly-found Feynman-Kac formulas and some associated results.
Year: 2018
Name: Lorenzo Riva
Institution: Creighton University
Subject area(s):
Title of Talk: Feynman Operational Calculus
Abstract: The forthcoming paper "Combining continuous and discrete phenomena for Feynman's operational calculus in the presence of a $(C_0)$ semigroup and Feynman-Kac formulas with Lebesgue-Stieltjes measures" (by L. Nielsen, to appear in Integral Equations and Operator Theory) contains, as its main result, an evolution equation which serves to describe how Feynman's operational calculus evolves with time in the presence of a $(C_0)$ semigroup of linear operators. There are several examples in this paper which give rise to so-called, Feynman-Kac formulas with Lebesgue- Stieltjes measures (first investigated from a function space integral point of view by M. L. Lapidus in the late 1980s). However, due to the different approach, the Feynman-Kac formulas obtained in the paper by Nielsen have some significant differences from those obtained by Lapidus. An associated operator differential equation (essentially a nonhomogeneous Schrodinger's equation) is also obtained in Nielsen's paper. This talk will concentrate on the explanation of the newly-found Feynman-Kac formulas and some associated results.
ID:
533
Year: 2019
Name: Lorenzo Riva
Institution: Creighton University
Subject area(s): Analysis, PDEs
Title of Talk: Low Regularity Non-$L^2(\mathbb{R}^n)$ Local Solutions to the gMHD-$\alpha$ system
Abstract: The Magneto-Hydrodynamic (MHD) system of equations governs viscous fluids subject to a magnetic field and is derived via a coupling of the Navier-Stokes equations and Maxwell's equations. It has recently become common to study generalizations of fluids-based differential equations. Here we consider the generalized Magneto-Hydrodynamic alpha (gMHD-$\alpha$) system, which differs from the original MHD system by the presence of additional non-linear terms (indexed by the choice of $\alpha$) and replacing the Laplace operators in the equations by more general Fourier multipliers with symbols of the form $-\vert \xi \vert^\gamma / g(\vert \xi \vert)$. In \cite{penn1}, the author considered the problem with initial data in Sobolev spaces of the form $H^{s,2}(\mathbb{R}^n)$ with $n \geq 3$. Here we consider the problem with initial data in $H^{s,p}(\mathbb{R}^n)$ with $n \geq 3$ and $p > 2$, with the goal of minimizing the regularity required to obtain unique existence results.
Year: 2019
Name: Lorenzo Riva
Institution: Creighton University
Subject area(s): Analysis, PDEs
Title of Talk: Low Regularity Non-$L^2(\mathbb{R}^n)$ Local Solutions to the gMHD-$\alpha$ system
Abstract: The Magneto-Hydrodynamic (MHD) system of equations governs viscous fluids subject to a magnetic field and is derived via a coupling of the Navier-Stokes equations and Maxwell's equations. It has recently become common to study generalizations of fluids-based differential equations. Here we consider the generalized Magneto-Hydrodynamic alpha (gMHD-$\alpha$) system, which differs from the original MHD system by the presence of additional non-linear terms (indexed by the choice of $\alpha$) and replacing the Laplace operators in the equations by more general Fourier multipliers with symbols of the form $-\vert \xi \vert^\gamma / g(\vert \xi \vert)$. In \cite{penn1}, the author considered the problem with initial data in Sobolev spaces of the form $H^{s,2}(\mathbb{R}^n)$ with $n \geq 3$. Here we consider the problem with initial data in $H^{s,p}(\mathbb{R}^n)$ with $n \geq 3$ and $p > 2$, with the goal of minimizing the regularity required to obtain unique existence results.
ID:
259
Year: 2009
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Algebra, elementary number theory
Title of Talk: Sequences and their annihilators
Abstract: Annihilating polynomials have been widely used in geometry and to study sequences over fields and over the integers Z. We use the same simple ideas to study sequences over Z modulo n. There are surprising difficulties, surprisingly nice results and an open conjecture. We can demonstrate some applications to recurrence sequences like the Fibonacci and Lucas numbers, or discrete dynamical systems. Joint work with John Gillespie. Prerequisites: ring, ideal, quotient ring, Chinese Remainder theorem - suitable for undergraduates with a first course in algebra.
Year: 2009
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Algebra, elementary number theory
Title of Talk: Sequences and their annihilators
Abstract: Annihilating polynomials have been widely used in geometry and to study sequences over fields and over the integers Z. We use the same simple ideas to study sequences over Z modulo n. There are surprising difficulties, surprisingly nice results and an open conjecture. We can demonstrate some applications to recurrence sequences like the Fibonacci and Lucas numbers, or discrete dynamical systems. Joint work with John Gillespie. Prerequisites: ring, ideal, quotient ring, Chinese Remainder theorem - suitable for undergraduates with a first course in algebra.
ID:
279
Year: 2010
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): ODE, recurrence, power series, experimental mathematics
Title of Talk: Recurrences, power series, and ODE
Abstract: A three-term recurrence is connected to a power series, which solves a second-order ODE. The recurrence can be helpful in solving the ODE explicitly, and in approximating the power series. As is well-known, its growth rate is related to the radius of convergence of the power series. We will use a simple example straight from the textbook to investigate this in the case of a recurrence with *non-constant* coefficients. While the growth rate turns out to be surprisingly resistant to attack, it has great potential to be explored experimentally as well as theoretically - an opportunity for open-ended student projects.
Year: 2010
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): ODE, recurrence, power series, experimental mathematics
Title of Talk: Recurrences, power series, and ODE
Abstract: A three-term recurrence is connected to a power series, which solves a second-order ODE. The recurrence can be helpful in solving the ODE explicitly, and in approximating the power series. As is well-known, its growth rate is related to the radius of convergence of the power series. We will use a simple example straight from the textbook to investigate this in the case of a recurrence with *non-constant* coefficients. While the growth rate turns out to be surprisingly resistant to attack, it has great potential to be explored experimentally as well as theoretically - an opportunity for open-ended student projects.
ID:
548
Year: 2019
Name: Christian Roettger
Institution: Iowa State University
Subject area(s):
Title of Talk: Balanced Numbers and Balanced Primes
Abstract: Balanced numbers are odd natural numbers n which have an equal number of 0s and 1s in the periodic part of the base-2 representation of their reciprocal 1/n. We present some insights about balanced numbers that use just elementary Number Theory like the Quadratic Reciprocity Theorem. In particular, if a prime p is congruent to 3 or 5 modulo 8, then p is balanced. If a prime p is congruent to 7 modulo 8, then p is not balanced. All powers of p are balanced iff p is. The case of primes congruent to 1 modulo 8 is much more difficult. Hasse made a breakthrough in 1966, showing that the balanced primes have a Dirichlet density of 17/24. We have refined Hasse's result slightly. Another question is how big is the set of balanced numbers (not only primes) less than x? Using a method due to Landau, we can show that this is bounded above by C x/log^(1/4) (x) and below by D x / log^(3/4)(x), with constants C, D > 0. I solemnly promise that I won't go into the gory detail, only highlight the beautiful and accessible parts of the subject. The second part of the talk is joint work with Joshua Zelinsky.
Year: 2019
Name: Christian Roettger
Institution: Iowa State University
Subject area(s):
Title of Talk: Balanced Numbers and Balanced Primes
Abstract: Balanced numbers are odd natural numbers n which have an equal number of 0s and 1s in the periodic part of the base-2 representation of their reciprocal 1/n. We present some insights about balanced numbers that use just elementary Number Theory like the Quadratic Reciprocity Theorem. In particular, if a prime p is congruent to 3 or 5 modulo 8, then p is balanced. If a prime p is congruent to 7 modulo 8, then p is not balanced. All powers of p are balanced iff p is. The case of primes congruent to 1 modulo 8 is much more difficult. Hasse made a breakthrough in 1966, showing that the balanced primes have a Dirichlet density of 17/24. We have refined Hasse's result slightly. Another question is how big is the set of balanced numbers (not only primes) less than x? Using a method due to Landau, we can show that this is bounded above by C x/log^(1/4) (x) and below by D x / log^(3/4)(x), with constants C, D > 0. I solemnly promise that I won't go into the gory detail, only highlight the beautiful and accessible parts of the subject. The second part of the talk is joint work with Joshua Zelinsky.
ID:
64
Year: 2004
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number theory, exponential sums
Title of Talk: Uniform distribution and invertible matrices
Abstract: Uniform distribution is usually known as a property of sequences xn in the unit interval, like n alpha modulo 1, where alpha is irrational. We will present an example of uniform distribution in the unit square, explain the handy Weyl criterion used to prove uniform distribution, and conclude with an application to invertible 2x2 - matrices over the integers.
Year: 2004
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number theory, exponential sums
Title of Talk: Uniform distribution and invertible matrices
Abstract: Uniform distribution is usually known as a property of sequences xn in the unit interval, like n alpha modulo 1, where alpha is irrational. We will present an example of uniform distribution in the unit square, explain the handy Weyl criterion used to prove uniform distribution, and conclude with an application to invertible 2x2 - matrices over the integers.
ID:
331
Year: 2012
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Multivariate Calculus, numerical mathematics
Title of Talk: Calculus III projects for Undergraduates
Abstract: Multivariate Calculus lends itself particularly well to explorations on the computer. Examples include Newton's method, Steepest Descent, two-dimensional Riemann sums, Euler's method for differential equations. Each of these can be presented in various appealing contexts and is immediately plausible for a student who understands the core concepts of the derivative of a multivariate function and Riemann sums, respectively. On the other hand, exploring the 'approximation' aspect of Calculus with paper and pencil and even with a calculator is less satisfactory than using a computer, especially if powerful mathematical software is available (eg SAGE, R, Matlab, Maple, Mathematica). Ideally, the results can be presented in an appealing graphic, and we'll show examples of student work. Finally, we do not assume any programming skills, but this kind of small project is a great opportunity to learn them.
Year: 2012
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Multivariate Calculus, numerical mathematics
Title of Talk: Calculus III projects for Undergraduates
Abstract: Multivariate Calculus lends itself particularly well to explorations on the computer. Examples include Newton's method, Steepest Descent, two-dimensional Riemann sums, Euler's method for differential equations. Each of these can be presented in various appealing contexts and is immediately plausible for a student who understands the core concepts of the derivative of a multivariate function and Riemann sums, respectively. On the other hand, exploring the 'approximation' aspect of Calculus with paper and pencil and even with a calculator is less satisfactory than using a computer, especially if powerful mathematical software is available (eg SAGE, R, Matlab, Maple, Mathematica). Ideally, the results can be presented in an appealing graphic, and we'll show examples of student work. Finally, we do not assume any programming skills, but this kind of small project is a great opportunity to learn them.
ID:
372
Year: 2013
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory, Diophantine Geometry, L-functions
Title of Talk: Geometric distribution of primes in Z[sqrt(2)]
Abstract: It all starts with the question: what can we say about integers a, b such that a^2 - 2b^2 is a prime? We will show some ways to make this question more precise - in particular, we study the distribution of the corresponding points (a,b) in the plane. The fundamental tool is the ring Z[sqrt(2)], and from there we make connections to analytic number theory (L-functions, Hecke characters) which arise very naturally - this is the context where Hecke invented 'Hecke characters', and they are much easier to understand here than when you read about them in MathWorld.
Year: 2013
Name: Christian Roettger
Institution: Iowa State University
Subject area(s): Number Theory, Diophantine Geometry, L-functions
Title of Talk: Geometric distribution of primes in Z[sqrt(2)]
Abstract: It all starts with the question: what can we say about integers a, b such that a^2 - 2b^2 is a prime? We will show some ways to make this question more precise - in particular, we study the distribution of the corresponding points (a,b) in the plane. The fundamental tool is the ring Z[sqrt(2)], and from there we make connections to analytic number theory (L-functions, Hecke characters) which arise very naturally - this is the context where Hecke invented 'Hecke characters', and they are much easier to understand here than when you read about them in MathWorld.