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. Math Seminar Schedule -- Spring
2015
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WEEK |
DATE |
Speaker and Title |
Abstract |
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1 |
Wed,
Jan 14 |
Introduction
and Policies |
Not
Applicable |
|
2 |
Wed,
Jan 21 |
Damiano Fulghesu Introduction to Zermelo-Fraenkel Axioms (Part 1) |
Sets are the basic objects of
mathematics. More precisely every mathematical statement can be written only in
terms of sets and symbolic logic. But we have a problem. If sets are the fundaments
of mathematics, what are the objects of which sets are made? They are sets as
well! As an example, consider the set N of natural numbers. Clearly 2 is
an element of N, but can we see 2 as a set? Can we give a meaning to
the expression 2∩3 ? The Zermelo-Fraenkel axioms allow us to present every mathematical object as a set
and they provide a consistent theory for sets and ultimately for mathematics
as a whole. In these two seminars, we present the Zermelo-Fraenkel
axioms and show how to write consistent definitions avoiding dangerous
paradoxes. |
|
3 |
Wed,
Jan 28 |
Damiano Fulghesu Introduction to Zermelo-Fraenkel Axioms (Part 2) |
Sets are the basic objects of
mathematics. More precisely every mathematical statement can be written only
in terms of sets and symbolic logic. But we have a problem. If sets are the
fundaments of mathematics, what are the objects of which sets are made? They
are sets as well! As an example, consider the set N of natural numbers.
Clearly 2 is an element of N, but can we see 2 as a set? Can we give a
meaning to the expression 2∩3 ? The Zermelo-Fraenkel axioms allow us to present every mathematical object as a set
and they provide a consistent theory for sets and ultimately for mathematics
as a whole. In this second seminar, we present the last four Zermelo-Fraenkel
axioms. In particular, we will prove that the universe is not a set and we
will define the set of natural numbers. |
|
4 |
Wed,
Feb 4 |
Adam Goyt The
Magic of de Bruijn Sequences |
In the universe of
mathematics there are many worlds. Of these, there’s the world where we apply
our theory, the world where the theory is interesting for its own sake, and
the world where mathematics is entertaining to the uninitiated. Some mathematical
objects manage to live in all of these worlds at once. In this talk we will discuss
de Bruijn sequences, which I claim manage this graceful
dance between worlds. We will start in the world of entertainment and find
ourselves naturally transported to the world of mathematics for the sake of mathematics.
In this world we will prove that de Bruijn
sequences of any size exist and find out how many there are. We will then
scratch our heads and wonder how we can apply de Bruijn
sequences, and in an instant we will find ourselves in the world of
mathematics as applied to computer science, engineering, and biology. A short
discussion about applications to computer science and engineering will
quickly lead us whence we came. We will finish by
discussing a bit about how mathematicians are explorers, who move between
these worlds as their needs arise. Whether they are solving problems in
industry or have just found a curious object, mathematicians are explorers
who search for truth, proof, and fun! |
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5 |
Wed,
Feb 11 |
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6 |
Wed,
Feb 18 |
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7 |
Wed,
Feb 25 |
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8 |
Wed,
Mar 4 |
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9 |
Wed,
Mar 11 |
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No
Classes: March 16th – March 20th Spring Break |
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10 |
Wed,
Mar 25 |
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11 |
Wed,
Apr 1 |
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12 |
Wed,
Apr 8 |
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13 |
Wed,
Apr 15 |
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Last Day
to Withdraw – Monday, April 20th by 4:00pm |
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14 |
Wed,
Apr 22 |
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15 |
Wed,
Apr 29 |
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