(Click on title to view those with a video.)

**Some Irrational Numbers
Sang Lee (9/18/19)**

In textbooks for intermediate algebra, college algebra, trigonometry, and precalculus, it is common to find the directions for exercises such as “Solve each equation. If the answer is not exact, round to four decimal places.”, or “Solve each equation. Give irrational solutions as decimals correct to the nearest thousandth.”

Do students know whether a solution they obtained is rational or irrational? Would students recognize an irrational number when they see it? Technology does not help as a graphing calculator can display only a finite number of digits and, at times, a calculator can mislead students in determining irrationality of a number.

In this talk, we will review some common irrational numbers that students may encounter in a course mentioned above.

**Bayes' Theorem: Using Probability Theory to Quantify Uncertainty
Luke Ellison (4/17/19)**

Bayes' theorem is a probabilistic equation that allows us to update our prior beliefs in the face of new evidence. This talk will explore the historical development and application of Bayes' theorem including unique problems that it has helped solve. Specific areas of application include World War 2 codebreaking, authorship of the Federalist papers, and quantifying degrees of certainty in historical claims.

**Systems of Linear Equations, Linear Programming, and the Simplex Method****Alejandro Saldivar (3/27/19)**

The Simplex Method is used to optimize logistic problems such as transportation scheduling. In this talk we review some history and insight into the method from geometric and vectorial points of view. This talk is suitable for anybody with intermediate algebra background.

**Mathematical Forecasting and Classroom Resources
Brian Hadley (2/21/19)**

Forecasting student attendance in class has allowed for a reduction of wasted paper. Each semester I print quizzes, test, and worksheets for class use. Unfortunately, some of this paper is wasted primarily due to absent students. As a solution to this problem, I began forecasting student attendance, greatly reducing the amount of wasted printing.

Forecasting is a mathematical model that allows for a prediction of future trends. We will examine various forecasting methods that can provide reliable guidelines to classroom attendance trends, and result in the reduction of paper waste.

**De Montmort’s Matching Problem
Branden Wilson (1/23/18)**

Probability theory originated in the analysis of games of chance, beginning with the correspondence of Pascal and Fermat on dividing stakes in games of dice (1654-1660), and continuing with the first book on probability, Huygens’s ‘On Reasoning in Games of Chance’ (1657). Pierre Raymond de Montmort extended this work in his 1708 ‘Essay on the Analysis of Games of Chance,’ in which he considered probabilities in popular games of cards and dice. Among the card games he analyzed was Treize (or Recontre). It is for this analysis that de Montmort’s matching problem is named. After a few rounds of Treize, I will present a solution to the problem using the inclusion-exclusion principle developed by Nikolas Bernoulli.

**The Math Behind the Foldability of RNA
Katrina Teunis (11/13/18)**

This summer I was given funding to do some undergraduate math research on the mathematical patterns in how RNA folds. RNA, much like DNA, is made up of four building blocks called nucleotides: Adenine, Guanine, Cytosine, and Uracil. These nucleotides form a string that likes to fold in on itself and bond together - Adenine with Uracil and Guanine with Cytosine. So, the order and number of nucleotides present will determine how many ways the string of RNA can fold. By assigning these properties to letters, we can study this in a general context. Doing this I was able to find several new ways of determining how many times a string will fold as well as how to build a string with a specific number of foldings. I was also able to find or strengthen connections between RNA and other areas of mathematics. In this talk I will walk through how RNA folds, what I found in my research, and how RNA connects to other areas of mathematics. This research was funded by the Modified Student Summer Scholars Program from the Office of Undergraduate Research at Grand Valley State University.

**Symmetries in the Alhambra****Rebin Muhammad (10/30/18)**

An Islamic geometric pattern is a two-dimensional wallpaper that is created by only using a compass and ruler. The history of Islamic geometric patterns dates back to the 8th century and can been seen in most Islamic countries, where it is used in decorating the walls of buildings and mosques. We will explore some of these patterns.

**Series and Probability DO Mix****John Dersch (9/26/18)**

Suppose you start adding 1 + 1/4 + 1/9 + 1/16 + ... and you just keep going. As you add more and more terms, your answers will approach a unique number. It’s easy to approximate this number, but finding its exact value is a historically famous and fascinating problem. This talk has two parts. In Part 1 we will show how Leonhard Euler first solved this famous problem in the 1730s. Part 2 reveals an unexpected appearance of Euler’s solution in our search for the answer to a question involving probability and relatively prime numbers.

**“Archimedes: The Sand Reckoner”
Jeff Powers (4/17/18)**

“There are some, King Gelon, who believe that the number of the sand is infinite in multitude…” begins *The Sand Reckoner,* a 3rd-century BCE manuscript by Archimedes of Syracuse (287-212 BCE). Limited by Greek numerals, Archimedes sought a new number system capable of expressing quantities larger than the amount of sand that could fill up the universe. Of course, to do this, he had to first determine the size of the universe. *The Sand Reckoner* is significant not only for the extraordinary mathematics it contains, but also for its profound insights into the history of science. It cites the earliest account we have of a heliocentric solar system, contains adjustments for solar parallax and the anatomy of a human eye, and is regarded as the world’s first research-expository paper. This seminar showcases Archimedes’ genius via a detailed analysis of *The Sand Reckoner*, demonstrating his place as the greatest mathematician of antiquity.

**The Language of Mathematics ****Katrina Teunis (3/21/18)**

Have you ever joked about math being a language you don’t understand? Have you ever wondered what the purpose was in learning algebra when you have absolutely no plans to use math in your future careers? Well, what if math really is a language, and treating it as one could both help you understand mathematics and why it applies to your daily life? Seeing math as the language it is can open the door to understanding why math works the way it does and how it is more than just manipulating numbers. This talk will answer the question “is math a language” and address how viewing math in this way will improve your ability to work with numbers, use logic in your daily life, and truly understand mathematics.

**God's Algorithm: A Simple Solution for the Rubik's Cube
Fisher Pham (2/14/18)**

The Rubik's Cube--a puzzle that seems impossible to solve, yet some have managed to solve it in mere seconds. Whether you know how to solve it or if you've spent hours twisting and turning it to no avail, you might have wondered, "Is there a simple pattern that I could repeat over and over to eventually solve the Rubik's cube?" This hypothetical pattern is called "God's Algorithm". In this talk, we will find out if "God's Algorithm" exists and discuss other mathematical aspects of the Rubik's Cube.

**A Graph Theory Approach to Seating People at Parties
Michael Santana (1/18/18)**

You're hosting a party with at least three people, and you want to seat everyone around a large table so that each person is friends with the person on their left and the person on their right. How do you know when you can do this? This seemingly innocent question turns out to be quite difficult to answer! On the other hand, the question becomes (MUCH) easier when you don't require that everyone be seated at the table (so you're okay with some people standing around). In this talk we'll consider both questions (focusing mainly on the second question), look at several extensions of these questions, and see how doing research in mathematics can be like playing the wooden block game, Jenga.

**Reassembling Pieces of a Figure to Form Other Ones****Alejandro Saldivar (12/6/17)**

Given two figures with the same area, can we always cut one into pieces so the pieces can be reassembled to form the second figure? We investigate this question and provide some very interesting examples. This talk is suitable for an audience with a wide range of math backgrounds.

**Measuring Fairness: Beyond the "Eyeball Test" for Detecting Gerrymandering****Meghan VanderMale**** ** **(11/15/17)**

At the beginning of October, the Supreme Court heard oral arguments for the case of Gill v Whitford. It is one of the only cases on partisan gerrymandering to reach the Supreme Court and it challenges the redistricting of Wisconsin following its 2010 census. In this landmark case, a relatively simple mathematical measure called the *efficiency gap* was featured. This talk will discuss the efficiency gap and explore what exactly it measures and where it may fall short of being a miracle gerrymander measure. We will also discuss other mathematical measures that apply to gerrymandering cases and the challenges of using them in legal settings. The mathematics involved is very accessible and requires no previous math background, nor is it necessary to know much about gerrymandering. The talk will be of particular interest to students of mathematics, government, political science, law, and statistics. You are encouraged (though not required) to bring a laptop or iPad as a portion of the talk will have computer interactive elements.

**Undefined
Andrea Hayes**

**(10/18/17)**

Division by zero is often confusing and misinterpreted. Is 1/0 undefined or infinity? The answer often depends on who you ask and can lead to lively discussions, even arguments. The source of such discussions usually resides in the difference between actual division by 0 and what happens when the denominator approaches zero. This talk will provide an in-depth look at the complexity of division by zero at various levels of mathematics.

**An Investigation of Angles, Polygons and Mosaics****Javier Ronquillo ** **(9/21/17)**

Have you noticed that the New Year’s Eve ball that comes down every year in Times Square is not perfectly round? It is really made out of a bunch of smaller triangles! Could we make a ball like this using just stop signs? Have you noticed that soccer balls are hybrids of pentagons and hexagons? Could we do a hybrid ball with stop signs and triangles?

All these questions have to do with arranging regular polygons (these arrangements need not form a ball; for example, the polygons could also be sitting on a wall). We will call one of these kinds of arrangements a *mosaic*. Throughout history mosaics have been some of the most beautiful pieces of art, and mathematics is used to help create their harmony and beauty.

In this talk we will explore the questions listed above and many more. This material is accessible to everyone and provides a great opportunity to see math and art interact.

**The Open Gate of Mathematics: From the Alhambra to Escher
Jeff Powers **

**(4/20/17)**

In 1922, a 24-year-old artist named M.C. Escher visited the Alhambra, a 13th-century Moorish fortress and palace in Granada, Spain. The stunning Islamic design and geometric patterns overwhelmed the young artist, who began a 50-year obsession with dividing the plane. Today, Escher’s name is synonymous with tessellations, symmetry, and impossible shapes. His art’s mathematical structure has affected fields as far-reaching as combinatorics, graph theory, non-Euclidean geometry, and crystallography. This seminar focuses on Escher’s exploration of the two-dimensional plane and his link to the Moorish artisans of the past, begging the question: Were these artists doing math?

**The Origins of Numbers
José Garcia**

**(4/18/17)**

Every time we wonder if there is enough money to buy that new iPad AND groceries, numbers are used. We take for granted what it means to do basic arithmetic and, even more so, why the numbers came to be the way they are. Come join us in looking into the origins of numbers and why they look the way they do today!

**Math Hippies - The Pythagoreans
Carolyn Evans (4/13/17)**

Once upon a time, in an Italian seaport far far away, a strange cult of young aristocrats arose under the leadership of the mystical and mysterious Pythagoras...

The Pythagoreans were a philosophical society with some pretty radical world views and hippie-esque habits. They believed “that the elevation of the soul to union with the divine occurs by means of mathematics”, and that being strict vegetarians, abstinent from alcohol, and keeping no personal belongings would help them reach this goal.

This seminar will cover some of the philosophical foundations, famous legends, mathematical discoveries, and longstanding impacts that this group accomplished thousands of years ago.

**Community Structure in Networks
Duy Duong-Tran (4/5/17)**

The past two decades have witnessed tremendous growth in complex network analysis, as social and biological interactions, and the world-wide web, can be modeled in this framework. In this talk, we will survey different methodological approaches used to analyze community (cluster) structure in complex networks. We will also look at classical bi-section (two-cluster) network models and apply algebraic Eigen decomposition to analyze such networks.

**π, My Favorite Number
Nancy Forrest (3/14/17)**

One might argue that there is an infinite supply of interesting numbers. But no other number has generated as much curiosity, international competition, and mathematical passion as π. Plus it even boasts a holiday; Pi Day is on 3/14. This talk will include highlights of the history of π, how it was named, calculation of its value, and various ways people have memorized some of its digits.

**Mathematics in the Tower of Hanoi**

**Sang Lee (2/23/17)**

The Tower of Hanoi puzzle was first introduced by the Frenchman M. Claus in 1883. The puzzle has been popular ever since, and it can be found in toy/game shops around the world. The puzzle has drawn interest from a wide range of people, especially those who plan to study computer science. In this math seminar we will look at some fascinating, beautiful and powerful mathematics hidden in the Tower of Hanoi, along with those mathematicians related to the puzzle. Tower of Hanoi puzzles will be available for those attending the seminar.

**Why People Trust Statistics
Steve Harris (1/25/17)**

Many students in an introductory Statistics course sail along fine until “Distribution of a Sample Mean” sinks their boat. After failing to find an illustration that explained the concept in a way I could use with both math-oriented and non-math-oriented students, I built my own. The result is an Excel spreadsheet that visually demonstrates the power of the Central Limit Theorem.

**Probability: Curves Inspired by the Cosmos
Bethany Austhof (12/7/16)**

In this seminar, we will look at the applications of Calculus in the field of Statistics. Topics of discussion will include how we can derive exact probabilities using integration techniques, how to determine the mean of a continuous random variable using the center of mass formula, and a look at the derivation of the normal curve distribution function.

**Compass-Only Geometric Constructions
Alejandro Saldivar (11/15/16)**

In the geometry of straightedge and compass constructions, it turns out that the straightedge is not necessary. This math seminar will cover the following:

- a bit of history involving compass-only geometry
- why a collapsible compass is sufficient
- some examples of constructions with just a compass
- at least one reason why the straightedge is superfluous in the geometry of straightedge and compass

**Some Sums
John Dersch (10/26/16)**

In the process of preparing assignments for a Precalculus course, I encountered a pair of intriguing problems. Their ultimate purpose was this: If you keep adding the numbers 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ∙ ∙ ∙, how many must you add to exceed a given number? My talk will range over a variety of topics related to this question, including sums, infinite series, logarithms, prime numbers, twin primes, factorials and the Gamma function, history, physics, music, the Black Death and a #1 hit from the late 60s.

**Magical Mathematics****Meghan VanderMale (9/27/16)**

In 1959, when he was 14 years old, Perci Diaconis dropped out of high school to travel with a legendary magician, a slight-of-hand expert. Where did this bold move lead him? It brought him to the world of mathematics, which he found was the key to being able to improve and create his own magic tricks. Now Diaconis is a Mathematics and Statistics professor at Stanford University and has teamed up with Ron Graham, former trampolinist and juggler turned mathematician, to write about the mathematical ideas behind magic tricks. We will be looking at a few of the tricks that they discuss in their book *Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks. *In this talk we will learn about gray code, linear-shift registers, de Bruijn sequences and graphs, and other mathematical ideas behind magic tricks such as *Coluria* and the *Royal Hummer*. Not only will you learn some interesting math, you’ll also learn the secrets of some quite elegant card tricks! Most of the talk is accessible to anyone, but those interested in computer science and/or advanced algebra will find a few gems in these tricks.

**How Hilbert's Infinite Hotel Can be Used to Evaluate Divergent Series****Logan Gaastra (4/20/16)**

Everyone knows that infinity plus one is still infinity, but did you know that we can use this property to assign values to divergent series? We will use the famous thought experiment of David Hilbert and basic knowledge of hyperreal numbers to systematically assign real values to certain divergent series. We will also look at other famous examples of attempts to assign values to divergent series, and examine their veracity against our system.

**Stories of Statistics
Curt Baragar (3/23/16)**

We will take a brief walk through the history of statistics, occasionally stopping off the path to take a look at some of the colorful characters who have contributed to this field. Also, along the way we will consider questions such as: How much longer should you expect to live? What do you mean by “average”? What do actuaries do? What is a p-value, what is a double-blind study, and why are these important?

**The Bean Machine, Sir Francis Galton, and the Central Limit Theorem in action!****Brian Hadley (2/24/16)**

English statistician Sir Francis Galton invented the Galton Board, also known as the Bean Machine, to demonstrate the Central Limit Theorem. This mechanical device drops balls onto a series of pegs. At each level, as the ball hits a peg, the ball must bounce left or right creating an exciting visual display. This experiment in binomial probabilities gives us insight into how seemingly random events are actually tied to the normal distribution.

**“Out of Control” in Statistical Process Control: Meaning and “Prevention”
Duy Duong-Tran (1/27/16)**

The practice of six-sigma is well-established in many areas of industry that involve repetitive processes and outputs. In this talk we will discuss control chart performance, what could happen if a process is "out-of-control", and recent developments in control charting techniques. Surprisingly, statistical control models are not only implemented in traditional industries such as automotive and pharmaceutical, but also in unexpected areas such as health care management and health surveillance.

**The Stable Marriage Problem: An Intersection of Social Choice and Mathematics****Grant Jenkins (12/10/15)**

The problem: Imagine that we are playing matchmaker. We have 10 male clients and 10 female clients who wish to be matched with someone of the opposite sex. Each of the 20 clients gives us a list of rankings of who they wish to be matched with. How do we use these lists to arrange 10 happy marriages?

This talk will rely on a field of mathematics called graph theory to match together people based upon a list of preferences. We aim to create a “stable marriage” in order to cater to as many individuals’ preferences as possible. This is accomplished with the Gale-Shapely Algorithm, which allows us to identify a definitive set of matchings. In reality, peoples’ rankings of each other - preferences - are not always strict and sometimes include indifferences. In this case, we can extend Gale-Shapely to find matchings. This introduces many new classifications of stability and gives us a glimpse into interactions between social choice and mathematics.

**Trigonometry: A Topic Full of Surprises****Dr. Radu Teodorescu (10/21/15)**

In this talk I will start with some less common theorems about triangles (!!) and go through several nontrivial examples of conditional identities. Finally, with the help of trig functions, I will introduce some special polynomials, including the Tchebycheff Polynomials. Using them we will end with two results: one about the values {cos(rp), sin(rp) : r ϵ Q} , and the other, a minimax property of Tchebycheff Polynomials, which will take us into advanced mathematics territory.

**Graph Labeling****Sang Lee (9/23/15)**

The concepts of graph labeling began about 50 years ago, and have been research topics for many mathematicians all over the world. While there are many different graph labeling techniques, in this seminar talk we will focus mainly on the three most popular graph labelings: a vertex labeling called *graceful* labeling, and edge labelings called *magic* and *super-magic* labeling. We will also investigate how these graph labelings are applied to graph decompositions and well-known magic squares.

**Triangles, Parallels, and Perpendiculars:** **A Story of Geometry
Steven Janke (4/16/15)**

One of the basic ideas in geometry is that when you add up all the angles in a triangle you get 180 degrees, but is this always true? Consider the earth and one line being the equator and two other lines being lines of longitude. If we pick two longitudinal lines that are perpendicular then these lines will form a triangle. However, this triangle has 3 right angles which add up to 270 degrees. Surely this must be a mistake, or some special case, or maybe there is something wrong with geometry…or could there possibly be alternative geometries?

Learn about the history of Hyperbolic Geometry, its creation and its discovery, and attempts to prove Euclid’s Parallel Postulate. Some of the major issues with newer geometries are finding logically consistent models, and we will explore some of the famous models for Hyperbolic Geometry and learn some of the basic constructions possible. We will finish with a qualitative investigation into curvature of a surface and what that means for geometry.

**Trigonometry in the Marine Corps****Gregory Metzner (4/15/15)**

As a high school student, I did not appreciate math. Upon entering the “real world”, I learned that math is integral and used everywhere, and I found that I can actually learn to enjoy math. As a Marine, I was taught to use basic mathematics on a daily basis. In preparation for a combat deployment, I investigated the mathematical concepts of polar and grid coordinates that could have readily been used, but were not. I wanted an answer as to how I could use math to make my job easier and more efficient. The deeper I investigated, the more dead ends I encountered, and was even told at one point that the type of math I wanted to learn just did not exist. I now know better, and have found the answer to my question. It lies in trigonometry. In my presentation, I will discuss the specific problems I want to solve, and the functions I can use to solve these problems. I will also discuss whether my new found math can actually be employed and used efficiently in the field, compared to the traditional mechanisms in place to solve these problems.

**Number Sense: A Biological Look at How Our Minds Create Mathematics****Andrea Hayes (3/26/15)**

How can an infant know that 1 plus 1 equals 2? Why is it that, even after years of school, many of us still aren't sure if 6 times 7 is 42 or 54? How can animals without a language know some elementary arithmetic? This talk will take a biological look at how the human mind creates mathematics and its implications on the teaching of mathematics.

**Equations!?! What Equations?** **or Arithmetical Methods of Solving Word Problems
Radu Teodorescu (2/26/15)**

Word problems are “le raison d’être” of beginning Mathematics, often one of its most important parts. Usually at this level, word problems are solved using equations or systems of equations. After writing an equation/system for a given word problem we solve it and – voilà! – the solution appears. This is a direct and effective method, but what we gain in simplicity, we lose in depth of understanding of intricate connections among elements of our problem.

By contrast, Arithmetical Methods of solving word problems may appear to be more difficult. A particular kind of problem may need a specific approach, which in turn requires mental gymnastics, but in the end surprising internal links may be revealed. Arithmetical Methods teach us not only to think in non-standard ways, but also to write and display ideas in non-conformist manners. The speaker will present specific Arithmetical techniques, and some of the most important methods (known to him ☺!!), for example, the Method of Reduction to Unit, the Method of Comparison, the Method of Additional Assumption, the Method of Inverse Route, etc.

**The Hungarian Algorithm: A Solution to the Assignment Problem****Brian Hadley (1/29/15)**

In this talk we will discuss the Assignment Problem: How do we optimize the assignment of employees to work tasks? The problem of assigning "individuals" to perform specific "tasks" has special characteristics and structure, which were cleverly exploited by Harold Kuhn in 1955 to produce an efficient method that generated an optimal solution. We will work out examples of the "Hungarian Algorithm," work together to solve the Assignment Problem, and examine Kuhn's paper describing his remarkable method.

**A Quest to find a One-to-One and Onto function from the line segment [0,1] to the square plane region [0,1]x[0,1]****Alejandro Saldivar (11/20/14)**

Many theorems in mathematics address the existence or non-existence of mathematical objects such as solutions to equations; however, finding an actual and precise mathematical object can be an exciting and, at times frustrating, quest. In this seminar we will talk about one-to-one and onto functions between sets, and the challenges involved in finding a one-to-one and onto function. Along the way, we will discuss decimals extensively.

**100 Years of Mathematics at GRJC/CC****John Dersch (10/15/14)**

In Fall 1914 the GRJC Mathematics Department offered one math class, taught by one instructor to fewer than twenty students. One hundred years later we offer 22 courses, taught by approximately 75 faculty to more than 5000 students each semester. We’ll discuss the people and courses that got us to where we are today. Emphasis will be on personalities, course development and anecdotes.

**Mathematics in the World of Industrial Engineers****Duy Duong-Tran (9/18/14)**

The influence of mathematics in our society is amazing. For example, mathematics plays a role in the infrastructure of the automobile industry (aerodynamic simulation through the use of math modeling), bioengineering (footwear design through piecewise linear interpolation and modeling), and the aviation industry (cubic spline interpolation at Boeing Research and Development to replace “lofting” technique).

This seminar will discuss the use of mathematics in the world of industrial engineering. Specifically, we will talk about Optimization Problems in the industry using Linear Programming (LP). Surprisingly enough, LP problems often do not employ any computer algorithm techniques, and most mathematics students are exposed to LP problems early in their careers without an official introduction to the topic. Well-known LP techniques can be applied to scheduling, transportation, assignment, capacity planning, network optimization models, project management, facility planning, and capital budgeting problems.

All of these reside under the applied mathematics field called Operations Research (OR). We will go through the technique of solving a couple of problems, and will be surprised at how much impact OR (or more generally mathematics) has upon the success of a manufacturing based corporation.

**One Aspect of Universal Design: Playing Games in Math Class****Monica Stevens and Barb Bouthillier (4/15/14)**

In an effort to engage all learners, in particular, kinesthetic learners, we collected and developed activities designed for instruction and practice in our Basic Math courses. These activities can be adapted for elementary or secondary use, or even for higher level classes. During this presentation, we will explain the process we used to create the activities, their implementation, and the results. Participants will play multiple activities and copies of them will be available electronically.

**Same Results, New Approach
Andrea Hayes (3/17/14)**

Basic mathematical operations such as addition, multiplication, division, and subtraction are now being presented to elementary school children using algorithms that are different than the traditional ones that many of us are used to. This talk will look at some of these different methods of computing sum, product, quotient, and difference, as well as discuss why these methods are being taught to students and how they may actually help with number sense and mathematical comprehension.

**“omg - i have to take a Mental Abuse To Humans class”
Pat Bentley and Erin Burke (2/19/14)**

Why do so many college students need remedial math? Why do so many of those students then continue to struggle with the subject? Why does the thought of even having to take a math class cause immediate anxiety? Two math teachers taught an Introductory Algebra course at a unique summer program through Ferris State University that was designed to combat those specific problems. During this seminar, they will share some of their strategies for teaching remedial math at the college level, emphasizing reading and writing in the discipline.

**Mersenne Primes and Perfect Numbers: A Love Story
Dan Garbowitz (1/22/14)**

Perfect numbers were known to the Greeks and have been studied since at least the 3rd century B.C. Marin Mersenne, a 17th century theologian and mathematician, developed a list of prime numbers, all with the same interesting form. Sometime later, Leonard Euler proved a fascinating statement that related the perfect numbers to the Mersenne Primes. During this seminar we will investigate this theorem in particular, and other number theory topics relating perfect numbers and Mersenne Primes.

**"Significant Figures: The Mathematics Behind their Significance. "
Dana Sammons (12/05/13)**

Significant Figures are

- those digits that ** carry meaning** contributing to its precision (Wikipedia)

- the number of

**digits in an expression (Whatis)**

*important*Just as many people believe what they read on websites like Wikipedia and Whatis when it might not be justified, often people believe that numbers are significant without carefully considering whether they deserve it.

In “The Pedagogy of Poverty vs. Good Teaching,” M. Abraham suggests we should provide students with a ** meaning-driven** curriculum. If we are to analyze, discuss and interpret the meaning of the results of calculations with any integrity, we must know with what precision we should assign the numbers.

This talk will look into the mathematics behind the “rules” associated with significant figures, including some of the suggested improvements people have made over time.

**"What's My Line?"
Tom Neils (11/13/13)**

Many scientific experiments are carried out to determine the mathematical relationship between two or more variables. Graphing the experimental data is often the most effective way of finding this mathematical relationship, because one can determine a curve of best fit for the trend in the data and also obtain a visual of the relationship between the variables. During this interactive seminar we will discuss the extent to which chemists will go to obtain a linear fit for their data and get some practice fitting the slope-intercept formula to various data sets.

**Old News About Percentages
Radu Teodorescu (10/17/13)**

Everyone has heard of percent. Beginning with pre-algebra, it is taught at GRCC in a variety of courses. Many of the current methods for teaching percent problems have been used for decades. This talk will submit an idea slightly different from traditional concepts. Some may agree with it, many others may have reservations and even objections. However, it is hoped that many in the audience will be surprised by some of the interpretations revealed during the talk.

**Abacus 101
Nancy Forrest (9/16/13)**

The Chinese abacus has been used to calculate and record numbers for over nine hundred years. This introduction to its use will include an overview of the rich history, as well as instruction on how to perform basic mathematical operations. There will be a hands-on opportunity to use the abacus … no batteries needed!

**Teaching Developmental Mathematics: It's Not Just About Math!
Betsy McKinney, Andrea Hayes, Shanna Goff, Linda Spoelman, Dominic Mattone and Paul Miltgen (4/23/13)**

Across the state and the country, the need for developmental mathematics courses is growing as more students are entering college underprepared. These students bring a unique set of challenges, skills, and experiences to the classroom. After a brief overview of current trends in developmental education, a diverse panel of experienced developmental mathematics teachers will discuss the various challenges they encounter when teaching the developmental student. Topics will also include best practices in the developmental classroom, technology in the developmental classroom, and the “other” skills developmental educators teach their students. Time will also be given for the audience to ask questions of the panel.

**Catastrophic Electrical Damage took place - let’s check the Math to see why!
Roger Berry (3/19/13)**

All protection from damage or injury due to electrical faults begins with determining the amount of potential fault current. Mechanical and thermal energy released in less than 4 milliseconds can produce catastrophic results. Electrical equipment and protective devices must be tested and rated to withstand the potential forces involved.

Electrical designs are evaluated for worst-case conditions to insure that equipment and people are adequately protected. Fault currents on both sides of the decimal point can result in destructive forces. Short circuits can result in destructive currents over 200,000 amps producing a blast that results in equipment damage and potential injury to personnel due to flash burns and sound, while ground faults as low as five milliamps can produce fibrillation resulting in death. In addition, lower level arcing faults can destroy electrical equipment or start a fire.

How do we do the math?

**Counting with Polynomials
Sang Lee (2/20/13)**

Do we obtain any valuable information from the product of polynomials? Specifically, what do coefficients and exponents tell us when polynomials are multiplied? In this talk, we introduce a counting technique that utilizes the coefficients and exponents in the product of polynomials. We then examine some counting problems such as determining the number of ways for different routes, muffin orders, changing a dollar, solutions to an equation, and partitions of an integer.

**What's Math Got to Do with It?
Yumi Watanabe (12/05/12)**

In this talk we will explore the world of mathematics. Beginning with our ability to sense quantities, we will survey various aspects of ideas and concepts that make up the world of mathematics, including numbers, algebra, calculus and areas of modern mathematics. Along the way we will ask and attempt to answer questions such as, "What is mathematics, anyway?", "What is it good for?", "Why is it so hard?" and "Does mathematics have anything in common with disciplines such as language arts and social sciences?" At the end of the talk, borrowing words of Sir Isaac Newton, a definition of mathematics (perhaps an unconventional one) will be given.

**Magic Squares
Brian Hadley (12/05/12)**

Magic squares have fascinated professional mathematicians as well as mathematical hobbyists for over 4000 years. The Lo Shu magic square with its uniqueness captures the symmetry and beauty of mathematics, Dürer's square backdrops his famous engraving *Melancholia*, and Benjamin Franklin constructed them to keep his mind sharp. We will explore a few magic squares and unlock some of their mysteries.

**Paradoxes: What Are They and Why Are They Significant?
Patrick Campbell (11/13/12)**

Consider the following statement: “This sentence is false.” Well then, if the statement is true, it must be false; and if the statement is false, then it must be true. What is going on here? The statement above is a version of the “Liar” or “Epimenides Paradox”, named after the ancient Greek Epimenides of Crete, who is believed to have once stated that all Cretans are liars. As interesting and puzzling as paradoxes of this sort may be, even more fascinating things arise when we investigate the paradoxes of mathematics and logic. In this seminar, we will look at some paradoxes relevant to mathematics and logic, attempt to understand what it is that creates such bizarre results, and discuss why paradoxes are significant mathematically, historically, and philosophically.

**To Infinity and Beyond
Kelly Rozin (10/23/12)**

A great poet, William Blake, once wrote, "To see the world in a grain of sand, and see heaven in a wild flower, to hold infinity in the palm of your hands, and eternity in an hour." One might think that these words are silly a paradox that can never exist, but others might think it’s possible. Can you really hold infinity in the palm of your hand? Is it tangible? Does it exist? This talk will go into the discovery and history of infinity and what it actually means to be infinite. It will also describe the different methods of proving infinity's existence and how it is used in the world of mathematics and our everyday lives.

**50 Centuries in 50 minutes (A Brief History of Mathematics)
John Dersch (9/19/12)**

How did we get the mathematics that is studied today? Who was responsible for major advances in the mathematics that we now take for granted? When and where did this work take place? Such questions will be addressed by tracing the development of mathematics from 3000 B.C. to the dawn of the 21st century. There will be time for questions and suggestions for further study will be made.

**Number Theory Potpourri
Tom Post (4/18/12)**

This informal talk will feature a collection of interesting topics from the branch of mathematics called *number theory*. Topics of discussion will include Collatz’s Sequence, the Golden Ratio, Fibonacci Numbers and Binet’s formula, Pythagorean Triples, Continued Fraction Expansions, and Solutions to Pell’s Diophantine Equation.

**Fractals and Chaos
Julia Moore and Tom Worthington (3/22/12)**

Beyond their captivating images, why are fractals so interesting to mathematicians? The answer comes from their unique history, recent discovery and their many interesting properties of symmetry, simplistic complexity and self-similarity. Fractals are very different from the lines and curves created by most simple equations, yet these complex graphs come from very basic functions that only reveal their complexity as they are recursively applied. Many mathematicians believe they may be used as a way of predicting seemingly "random" events in the natural world, and their applications have greatly improved the advances of the field known as Chaos Theory.

For the talk, bring in your TI-83 or TI-84 calculators and get programs that combine Newton's Method with fractals.

**Teaching Methods that Encourage Participation
Julia Moore and Melanie Forbes (2/21/12)**

Julia Moore and Melanie Forbes will discuss high (and low) - tech methods for keeping your students involved in the classroom. Discover the free online graphing software of Geogebra, and explore the creation of a community of mathematics teachers and students using Geogebra at GeogebraTube. Listen to a unique perspective on using whiteboards in the classroom as a teaching tool. Delve into the free software of Respondus and Studymate that can create Flash-cards, Quizzes and Jeopardy games that can be used as study tools for your classes.

**Buddha loves geometry… at least according to Japanese?
Wayne Hsieh (1/25/12)**

Sangaku (or San Gaku) are Japanese geometric puzzles carved on wood tablets that are used as offerings at Shinto shrines or Buddhist temples. The puzzles consist of circles and triangles utilizing concepts from Euclidean geometry, and they typically ask the solver to find the relationship between the circles and triangles.

In this particular Sangaku, we will be looking at three circles placed inside a particular right triangle, and will investigate the radii and areas of the circles.

**Why People Trust Statistics
Steve Harris (12/7/11)**

Many students in an introductory Statistics course sail along fine until “Distribution of a Sample Mean” sinks their boat. After failing to find an illustration that explained the concept in a way I could use with both math-oriented and non-math-oriented students, I built my own. The result is an Excel spreadsheet that visually demonstrates the power of the Central Limit Theorem.

By changing any of these variables – *population range, population size, sample size, number of samples * – you can watch the conclusion of the Central Limit Theorem develop before your eyes. This little app has proven quite useful in helping students understand why we’re willing to make significant decisions based on a small amount of sample data, and reinforces why the Central Limit Theorem indeed is central in the field of Statistics.

**Euler’s Formula for Polyhedra: The Second Most Beautiful Theorem in Mathematics
Dan Garbowitz (11/16/11)**

Euler’s formula for polyhedra is so simple that a grade school student can understand it, yet this simple formula remained hidden from mathematicians and great thinkers for over 2000 years! The results of the formula gave birth to a new branch of mathematics called topology. This talk will focus on the history of Euler’s formula and present two proofs of it. The proofs differ vastly in their arguments and each is quite beautiful. One will even use a second branch of mathematics that Euler is responsible for – graph theory.

**Mathematics is with me every time I shift
Brian Deurloo (10/19/11)**

In the world of manufacturing and design, mathematics is the backbone which governs the systems we build for use in the real world. As an engineer it is essential to understand how these theoretical models perform so that each design can be optimized to ensure flawless function in the presence of the many noise factors from manufacturing.

In this presentation we will look at the theoretical "nominal" design of an automatic transmission shift system through the eyes of the trigonometry and algebra that governs it. Synchronization of these "cord length" travels between the shift lever and transmission lever are critical to all of the aspects of the shift system function. Finally, we will use some computer generated normally distributed statistical distributions to add in the variability of the system components to understand how to bring the theory into real world practice.**Dynamical Systems, Andrei Markov, and the Stochastic Matrix
Brian Hadley (09/20/11)**

In a system with a finite set of variables we can use the powerful tool of a Stochastic Matrix to examine how the state of a dynamical system will change with time. It was the Russian mathematician Andrei Andreyevich Markov who set the groundwork for a completely new branch of probability theory, and launched the theory of the stochastic processes. Today stochastic processes are used to study social sciences, physics, biology, economics and differential equations. We will examine simple dynamical systems utilizing the stochastic matrix, and take a look at practical applications of stochastic processes.

**Mathematical Modeling and Electrical Engineering
Sam Schoofs (02/23/11)**

Electrical engineers use a wide range of mathematical models to represent the physical realities of voltages and currents in electrical circuits. This talk will focus on models of electrical circuits that use calculus, differential equations, and linear algebra. Some models from the field of telecommunications will also be discussed.

**Check Digit Schemes: An Application of Number Theory
Sang Lee (01/26/11)**

Identification numbers are used to represent products, accounts, documents or individuals. Since we (our society) rely heavily on identification numbers to transmit information, sooner or later a transmission error will occur. Thus, it is crucial to know when an identification number has been transmitted incorrectly. The check digit schemes are the mathematical methods that detect when the identification numbers have been transmitted incorrectly. In this talk, we will look at a few check digit schemes that are used currently and the mathematics behind them.

**Quaternions and Rotation Sequences
Kurtis Bell and Ryan Mammina (12/10/10)**

Consider a remote object in 3-dimensional space of which we wish to track at a point in time. It is reasonable to ask, what is the most efficient way for one to track such an object? The topic of this talk, quaternions, will give us the tools we need to answer the aforementioned question. We will begin this survey of an introduction to hyper-complex numbers and their origin. The goal of the talk will be to provide a comparative analysis of two different methods for tracking the said object. With this in mind, the audience will make the final conclusion as to which method is most efficient. Join us as we venture into the curious world of quaternion geometry.

**The Mathematics of Sliding Logs (A presentation on the development, use, and secrets of the slide rule.)
Roger Berry (11/18/10)**

This presentation will provide an understanding of how the slide rule performs mathematical calculations, and a working knowledge of its application as a precision instrument. A working model will be provided for attendees which will allow you to go "Slip Slidin' Away" to solve future math problems.

We will review the use of logarithms, or logs as they became known, to do complex calculations. The use of logarithm tables and the amazing leap to simplified use through sliding rules culminated in the slide rule as we know it today. Great advances in science took place between 1700 and 1970 as the slide rule was used to do multiplication, division, logs, roots, exponential values and trigonometric functions.

**The Mathematics of Apportionment (How the first president of MAA teamed with a U.S. Census Bureau Chief Statistician to take on Thomas Jefferson, Alexander Hamilton, James Dean, and Daniel Webster.)
Dana Sammons (10/20/10)**

This talk will introduce various methods used to make "fair" apportionments. Then we will discuss the methods used throughout the history of the U.S. to decide how many representatives each state should have in Congress. We will also try to address the question whether the current method is biased.

**What Is This e Thing?
John Dersch (9/22/10)**

The common answer that "e is approximately 2.718" says little about the nature of one of the most important numbers in mathematics. This talk will begin by examining numerical and geometric interpretations of e. We will then look at a proof of the irrationality of e (short and sweet), briefly outline a proof that e is transcendental (the full proof is really sweet but not short – an opportunity to experience a complete proof will be offered), and end with a discussion of the tantalizing question "Is e normal?" (sweetest of all, but maddeningly frustrating...).

**Mental Arithmetic
Tom Post (4/21/10)**

Some of us are a part of a generation that never were faced with making a calculation without a use of a hand-held calculator. As a result, many of the mental techniques in making either exact or approximate calculations have been lost to technological advances. This is not to disagree with the use of calculators (I literally love my calculator), but only to bemoan what seems to be lost at the expense of our progress. Memory work, normally expected in our grade schools, has diminished to the point where students in our college mathematics courses don't know their times tables. Lack of that fingertip information is the prime cause of frustration and failure in the elementary pre-algebra courses that now dominate, in number, the math courses that are taught as college courses.

This talk is meant to introduce the average math students a new way of approaching the task of mathematical calculations as well as to inspire the more advanced students by integrating algebraic techniques with these calculations without the use of the calculator.

**Extensions to Complex Numbers of Some Common Functions
Radu Teodorescu (3/18/10)**

After a succinct presentation of complex numbers, we will extend to complex numbers the exponential, trigonometric and logarithmic functions. How this extension is done, several new properties of these functions, and some unexpected implications will also be presented.

**What Happened in Vegas... (Probabilities and Expected Values Associated with Texas Hold'em)
Jennifer Borrello (2/17/10)**

The AMATYC (American Mathematical Association of Two-Year Colleges) Conference held in Las Vegas, Nevada in November of 2008 had several interesting presentations about probability. This talk will focus on the card game Texas Hold'em. There will be a brief introduction to the game followed by a discussion of the probabilities and expected values associated with starting hands.

**Rational Approximations of Square Root of 2 (An Introduction to Isosceles" Almost" Right Triangles)
Dave Friday (1/21/10)**

While visiting the Calculus and Physical Sciences Tutorial Lab last semester, a question was posed: for what value of n will the sum of the first positive n integers be a perfect square? A thorough investigation of the problem and the introduction of the concept an isosceles "almost" right triangle yielded a number of interesting results. One of the results involves a sequence of rational numbers that converges to square root of 2, yielding some excellent approximations.

**The Gamma Function and Other Neat Mathematical Things
Radu Teodorescu (11/12/09)**

In this presentation, we will talk about multiplication, or to put it another way, many kinds of products. The expression n! (read n factorial), the product of all integer numbers starting with 1ending with n, makes sense only for positive integers 1,2,3, ... The main topic of the presentation is how to define the n factorial function for non-integer numbers. This problem, solved almost three hundred years ago by Leonhard Euler, still keeps busy many mathematicians with its implications and open questions.

**Want To Teach Math?
Panel Discussion (10/21/09)**

Panelists: Dan Garbowitz, Donna Joseph, Gary Kemp, Marsha Potter, Jim Vidro

Are you thinking about teaching mathematics? Are you teaching mathematics currently at GRCC and ever wonder what it's like to teach mathematics in high schools or middle schools? This seminar is a panel discussion on teaching (primarily secondary) mathematics, intended for those who are interested in pre-college mathematics education. The panelists consist of current or retired high school math teachers who are willing to share their experiences in order to benefit future (and current) math teachers. If you are interested in teaching mathematics, come find out what they have to say! We hope to leave time at the end of the seminar to take questions from the audience.

**Regular Polyhedra
Sang Lee (09/16/09)**

A regular polyhedron is a 3-dimensional convex solid in which all faces are congruent polygons, and the same number of polygons meet at each vertex. The Greeks, especially Plato and his followers, studied these solids to such an extent that they became known as the "Platonic solids". Furthermore, the Greeks believed that there are only five regular polyhedra. However, in a recent publication of Math Horizons (by MAA), it declared that "A new Platonic solid has been discovered!" Did the Greeks overlook the 6th regular polyhedron? In this talk we investigate the number of regular polyhedra using Graph Theory.

**Infinity
Gary Slopsma (04/22/09)**

How can a person contemplate infinity? It may seem beyond human grasp, yet there exist mechanisms by which we may decipher the mysteries of the infinite. This talk will introduce some of these mechanisms, sauntering through history, set theory, and some concepts of functions along the way. We will conclude with some startling and mind-bending results regarding the size(s) of infinity.

**Puzzling Mathematics of Sudoku
April Russell (03/18/09)**

Sudoku is the latest craze in puzzles, and is played by entering digits from 1 to 9 to complete a partially filled 9 x 9 grid so that each digit appears exactly once in each row, column, and 3 x 3 sub-grid. There are numerous variations with additional restrictions, for example, Sudoku X, where the entries on each of the main diagonals are also distinct. In this talk, the results of my summer research on Sudoku variations will be presented, using permutations, rook polynomials, and equivalence relations.

**Fourier Series
Tom Post (02/19/09)**

Just as Maclaurin or Taylor series are used to represent continuous functions with an infinite series of polynomials, a Fourier series is used to represent a periodic function in terms of an infinite sum of sines and/or cosines. Since sine and cosine functions represent simple harmonic motion (pure tones), Fourier series become a very useful tool in analyzing more complicated wave forms such as those produced by musical instruments, showing that any periodic wave form can be reduced to a superposition of pure tones of varying levels of magnitude(modal analysis). To determine these levels, called Fourier coefficients, we make use of the orthogonal relationships of the sine and cosine functions. We will look at the methods used to determine these coefficients and also display some of the interesting mathematical identities that result.

**The Doomsday Algorithm – Need I Say More?
Tom Worthington (01/21/09)**

You know your own birthday, but do you know what day of the week you were born? What about historical events? What day of the week did they take place? The doomsday algorithm gives you a way to calculate the day of the week of any given date based on the Gregorian calendar. Come find out how this works!

**The Fastest Curve
Christopher Grow (12/11/08)**

If you were to slide an object down a ramp, what curve will get it to the bottom the fastest? The answer to this question, posed by Johann Bernoulli in 1696 as a challenge to the mathematical community– Isaac Newton, in particular – is called the brachistochrone and it is the topic of our discussion. We will explore Bernoulli's result and its connection to a different problem: If you were to slide an object down a ramp, what curve will get it to the bottom in the same time regardless of where you start it?

**How Do Calculators Calculate? - A Look at the CORDIC Algorithm -
Curt Baragar (11/13/08)**

How does your calculator know the answer to sin(13.873°) or ln(8.2)? You may be surprised to learn that modern calculators rarely use polynomial approximation techniques such as Taylor series. Instead, they rely on an algorithm developed in 1959 for use in navigational computers on the B-58 bomber aircraft. In this talk we will explore the CORDIC (COordinate Rotation DIgital Computer) algorithm used by handheld calculators from Texas Instruments, Hewlett-Packard, and others.

**Competitive Math: How to Become a Mathlete
David Friday (10/16/08)**

The purpose of this talk is to help encourage awareness of and desire to take the AMATYC Student Mathematics League exam through exposure to the different types of competitive math that exist. This talk will cover what competitions are out there and available to students, particular problems from previous competitions, problems from previous SML exams, and a general strategy for the competition itself. In addition, a short interview with a previous SML winner and GRCC student will help to answer questions students may have about getting involved.

**What's the Point?
John Dersch (09/18/08)**

Most of us take decimal fractions for granted and may think of them as nothing more than advice for simplifying computations. Indeed that was the primary reason they were developed, but a close look reveals that they influenced 17th century mathematicians' understanding of number, variable, the continuum and the development of calculus. In this talk we begin with the calculus of Newton and Leibniz, then travel back to the analytic geometry of Fermat and Descartes, ending at Simon Stevin's 1585 publication "L'arithmétique" and its appendix "De Thiende" (The Art of Tenths), with side trips to contributions from the Greeks, the Arabs and wherever else the road takes us.

**Generalized Binomial Coefficients and Modified Pascal's Triangle
Elliot LaForge (04/09/08)**

This talk begins with a quick review of sequences. In terms of sequences, some of the interesting patterns in Pascal's triangle will be explored. Beginning from the well-known relationship between Pascal's triangle and the coefficients in the binomial expansion of (x+y)n, more general binomial theorems will be investigated and derived. (The results in this talk were discovered by Elliot Laforge.)

**Curvatures of Surfaces – Why I Love Gauss
Yumi Watanabe (03/19/08)**

Curvatures of surfaces are quantities that describe how "curved" a surface is at each point. How do we quantify these? This notion will be developed from the similar notion in curves, highlighting the great contributions of Carl Friedrich Gauss in the area of mathematics called differential geometry. The talk will end with truly amazing theorems in differential geometry due to Gauss.