What we're about

Math Counts is a meetup to engage all things mathematical in a relaxed setting on the fourth Saturday of each month. We strive to make each event accessible to those with rudimentary math skills while also engaging those with more advanced knowledge, so join us no matter what your level of mathematical ability.

Math Counts brings together math aficionados, amateur and professional mathematicians and educators to engage all things mathematical. Our meeting topics range from the elementary to the profound, the practical to the philosophical, and the simple to the complex. Whether we are discussing books or on-line videos, hanging out to discuss recent mathematics news, enjoying mathematics activities, or otherwise imbibing the mathematical, we invite you to join us in a relaxing setting for stimulating polite conversations and activities to participate in the fabric of Philadelphia's vibrant Mathematics tapestry.

Mathematics is surprising, playful, stimulating and profoundly applicable to most aspects of life. Keith Devlin and others call it the science of patterns. Here are some quotes about the subject:

"If the modern world stands on a mathematical foundation, it behooves every thoughtful, educated person to attempt to gain some familiarity with the world of mathematics. Not only with some particular subject, but with the culture of mathematics, with the manner in which mathematicians think and the manner in which they see this world of their own creation."
--- William Byers

"A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." --- An Old French Mathematician quoted by David Hilbert

"But it should always be insisted that a mathematical subject is not to be considered exhausted until it has become intuitively evident."
--- Felix Klein

"I assert only that in every particular Nature-study, only so much real science can be encountered as there is mathematics to be found in it"
--- Immanuel Kant

"The greatest challenge today, not just in cell biology and ecology but in all of science, is the accurate and complete description of complex systems. Scientists have broken down many kinds of systems. They think they know most of the elements and forces. The next task is to reassemble them, at least in mathematical models that capture the key properties of the entire ensembles."
--- E. O. Wilson, Consilience, p.85.

Upcoming events (1)

The Pattern of Partial Variation for Finding Extrema

Online event

This topic will explore the pattern of partial variation for finding minima and maxima (extrema) in geometry. How can we find extrema by looking at the partial variation, the variation of just one or two variables.

In particular, this group exploration will examine Chapter 8 §1–6 on pages 121–131 (with an in depth focus on §5) and Examples 15–22 on pages 133–134 in George Pólya's "Mathematics and Plausible Reasoning: Induction and Analogy in Mathematics" https://archive.org/stream/Induction_And_Analogy_In_Mathematics_1_#page/n139/mode/2up .

Prerequisite: high school geometry and algebra.

To guide your preparation & participation, consider:

➀ Our first concern will be an in depth exploration of each others' understanding and interpretation of the text in §5 of Chapter 8 on pages 128–130 (https://archive.org/stream/Induction_And_Analogy_In_Mathematics_1_#page/n147/mode/2up). Bring your notes, questions, insights, difficulties, and critiques for these three pages of text.

● In the text, Pólya solves the problem of finding the maximum of the product of n parts into which a line segment of length l has been subdivided. On page 130, Pólya writes, "The reader can learn a great deal in clarifying the foregoing proof. Is it quite satisfactory?" At the event, we will explore your attempts to clarify the proof that Pólya sketches. We will also explore your attempts to assess if the proof is satisfactory.

➁ Our second concern will be an in depth look at the "Examples and Comments on Chapter VIII" #15–22 of Chapter 8 on pages 133–134 (https://archive.org/stream/Induction_And_Analogy_In_Mathematics_1_#page/n151/mode/2up).

• These problems invite you to exercise your knowledge and skill to resolve mathematical questions. Bring your partial solutions so we can work together to strengthen everyone's understanding. Through this practice, we will all come to understand the particular situations and the pattern of partial variation better. Even when none of us can solve all the problems, hopefully each of us will understand enough to fill in each others' gaps to give everyone a better idea about how each one works.

Pólya's book is in the public domain, so you can find free copies of it in PDF, EPUB, Kindle, text, and other formats at https://archive.org/details/Induction_And_Analogy_In_Mathematics_1_ (scroll down to the "Download Options"). The PDF version (without text) might give the best printed version.

In addition to the main material described above, the following passages introduce Pólya's approach in the book which will be useful but not strictly necessary for the event:

• The Preface on pages v–x https://archive.org/stream/Induction_And_Analogy_In_Mathematics_1_#page/n7/mode/2up , pay particular attention to §1–4.

• The very important Hints to the Reader on pages xi–xii https://archive.org/stream/Induction_And_Analogy_In_Mathematics_1_#page/n13/mode/2up .

• Chapter 1 on pages 3–11 https://archive.org/stream/Induction_And_Analogy_In_Mathematics_1_#page/n21/mode/2up , pay special attention to Example Problems 9–14 on pages 9–11 https://archive.org/stream/Induction_And_Analogy_In_Mathematics_1_#page/n27/mode/2up .

Past events (124)

Using Tangent Level Lines to Find Extrema

Online event

Photos (30)