Mathematical Sciences Information Session · Applied Mathematics Using mathematical tools to solve practical problems. Science Business Industry Mark Huber, CMC Mathematics at CMC

Mathematical Sciences

Information Session

Department of Mathematical SciencesClaremont McKenna College

August 31, 2012

1

Welcome to CMC Mathematical

Sciences!

Today we will:

• Introduce ourselves

• Tell you about our courses and programs

• Discuss some of the math-related resourcesand research opportunities available to CMCstudents

• Answer your questions

2

Who we are:

• Asuman Aksoy, functional analysis, teach-ing MATH 32 and MATH 135

• Gerald Bradley, matrix theory and matheducation, teaching MATH 30 and MATH 60

• Lenny Fukshansky, number theory anddiscrete geometry, teaching MATH 31

• David German, mathematical finance,teaching MATH 31 and MATH 109

• Mark Huber, applied mathematics andstatistics, teaching MATH 32H and MATH 151

• Chiu-Yen Kao, applied mathematics, teach-ing MATH 31 and MATH 111

3

• Arthur Lee, computer science, on sab-batical

• Emily Navarro, computer science, teach-ing CSCI 51

• Deanna Needell, applied mathematicsand statistics, teaching MATH 52

• Sam Nelson, algebraic topology and knottheory, teaching MATH 30 and MATH 55

• Mike O’Neill, analysis, teaching MATH 30

• Mariam Salloum, computer science, teach-ing CSCI 62

• John Sun, computer science, teachingCSCI 62

• Robert Valenza, philosophy of mathe-matics, teaching MATH 30

Mathematics at CMC

Mark Huber

Department of Mathematical Sciences

31 August, 2012

Mark Huber, CMC Mathematics at CMC 1/10

Everyone at CMC takes at least one math course

From the catalogAny course offered by the CMC department ofMathematical Sciences satisfies the general educationrequirement in mathematics. This includes courses incomputer science and statistics.

TranslationYou don’t have to take Calculus to satisfy therequirement.


What should I take as my first math course?Four introductory courses in the mathematical sciences

Pure Math

MATH 035

Calculus andDiscrete Models

MATH 038

Intro Stats

MATH 052

Intro Comp Sci

CSCI 051

The Calculus sequence

Calculus I

MATH 030

Derivatives

Calculus II

MATH 031

Integrals

Calculus III

MATH 032

Multivariable


What is Applied Mathematics?

Applied MathematicsUsing mathematical tools to solve practical problems.

Science Business Industry


MATH 038: Calculus and Discrete Models for Applications

Calculus andDiscrete Models

MATH 038

Applied mathematics course that surveys:

Calculus I

MATH 030

Calculus II

MATH 031

Calculus III

MATH 032

DifferentialEquations

MATH 111

Probability

MATH 151

StatisticalInference

MATH 152

StochasticProcesses

MATH 156

NumericalAnalysis

MATH 163

OperationsResearch

MATH 187


Who should take Math 038?

Math 038 is a good choice if you:Pre-med students who need one semester of calculusPeople who need a refresher before going into Calc III(Math 038)Planning to do work in math heavy fields (Econ, Sociology)Need familiarity with a variety of different areas


Should I take the Calculus sequence? Math 030, 031, 032

Folks who should take Calc I, II, or IIIKnow that you are going to be taking Multivariable CalculusPlanning to be a physics or math majorKnow that you want to take advanced probability/statisticsIf you want to be a quant someday


Jumping the gun

Past experience counts!No course credit for AP Calculus......but does allow you to move ahead in sequence4 or 5 on AB Calculus Exam = skip Calculus I4 or 5 on BC Calculus Exam = skip Calculus IIProgramming experience = skip Intro to CSTalk to a math sci prof if your situation is unusual

Still have to take a math course in Claremont


A typical major in applied math track

Someone who decided they liked probability...Calculus and Discrete Models (MATH 038)Calculus II (MATH 031)Calculus III (MATH 032)Linear Algebra (MATH 060)Math Analysis I (MATH 131)Probability (MATH 151)Intro to Comp. Sci (CSCI 051)Differential Equations (MATH 111)Complex Analysis (MATH 135)Monte Carlo Methods (MATH 153)Statistical Inference (MATH 152)Stochastic Process and Modeling (MATH 156)Intro to the Mathematics of Finance (MATH 109)











Another typical major in applied math track

Emphasis on differential equations:Calculus III (MATH 032)Linear Algebra (MATH 060)Math Analysis I (MATH 131)Probability (MATH 151)Intro to Comp. Sci (CSCI 051)Differential Equations (MATH 111)Complex Analysis (MATH 135)Partial Differential Equations (MATH 182)Scientific Computing (MATH 164 HM)Monte Carlo Methods (MATH 153)Fourier Analysis (MATH 131)








Pure math at CMC

Lenny FukshanskyDepartment of Mathematical Sciences

Claremont McKenna College

August 31, 2012

1

What is pure mathematics?

Pure mathematics studies abstract mathe-matical structures and relations among them.Historically, the numerous fundamental appli-cations of mathematics to science, technol-ogy, economics, and social sciences resultedfrom the advancement of pure math.

The major branches of pure math include:

• Abstract Algebra investigates structureand properties of sets of objects (groups,rings, fields, vector spaces, modules) un-der binary operations, such as additionand multiplication.

• Analysis studies the theories of di!eren-tiation, integration and measure, limits,infinite series, and analytic functions onsets of real and complex numbers.

2

• Geometry is concerned with questions ofshape, size, relative position of figures,and the properties of space.

• Number Theory studies the propertiesof numbers in general, and integers inparticular, as well as the wider classes ofproblems that arise from their study.

• Topology investigates properties of ge-ometric objects that are preserved undercontinuous deformations, such as stretch-ing without tearing or gluing.

Why study pure math?

• Math is beautiful!!!

• Pure math develops ones analytical think-ing and logical reasoning abilities like noother subject!

• Education in pure mathematics serves asfundamental grounding for a number ofcareers in science, engineering, finance,and law.

• According to the Department of Educa-tion studies, the number of math coursesa person takes in college is the single bestpredictor of their lifetime earnings.

3

Why study pure math at CMC?

• CMC has one of the strongest math de-partments among all liberal arts collegesin the country.

• We have an extensive number of o!eringsin mathematics, including many specialand advanced topics courses in a widevariety of mathematical disciplines.

• We o!er many exciting opportunities forundergraduate research in mathematics.

4

Typical pure math major at CMC

The core courses

MATH 30, 31, 32 – Calculus sequenceMATH 60 – Linear AlgebraMATH 131 – Real Analysis IMATH 135 – Complex AnalysisMATH 140 – Modern GeometryMATH 151 – ProbabilityMATH 171 – Abstract Algebra I

The elective courses (choose 4)

Analysis: MATH 130 - 139Geometry/Topology: MATH 140 - 149Probability/Statistics: MATH 150 - 159Algebra/Number Theory: MATH 170 - 179

5

Math resources at CMC and in the 5-C

• CMC math department operates a tutor-ing center with tutoring help availableSunday through Thursday from 8:00 to10:00 pm in Adams 208.

• The math departments of the ClaremontColleges are united under the auspicesof the Claremont Center for Mathe-matical Sciences (CCMS), which o!ersa wide range of mathematical programsand communication / collaboration op-portunities for students and faculty.

• CCMS operates an active weekly collo-quium and seminars series, which presenta great variety of mathematical talks.

• The 5-C main library has one of themost extensive mathematics collectionsin Southern California.

6

Computer Science at CMC

Mike O’Neill (for Art Lee)Department of Mathematical Sciences


August 31, 2012

1

General Education Requirements: Mathematics or Compute Science

!  Catalog: “Any CMC mathematics or computer science course”

!  CS courses available for freshmen: –  CSCI 51 Introduction to Computer Science –  CSCI 62 Data Structures and Advanced Programming (if you have

already taken a 51-equivalent) –  CSCI 52 Fundamentals of Computer Science (if you have already taken

both 51- and 62-equivalents)

CS Programs at the Colleges: All Available to CMC students

!  Computer Science Sequence at CMC –  Requires five CS courses and Discrete Mathematics –  Seamless transition to a dual or full major at Pomona or HMC

!  Dual Major in Computer Science –  Through Pomona

!  Full Major in Computer Science –  Through either Pomona or HMC

CS Courses At the Colleges !  CS 51, 52, and 62 at CMC or Pomona are equivalent to CS

5, 60, and 70 at Mudd (stay with one sequence though!)

!  After completing either of the above 3-course sequences, you can continue with the upper division CS courses at any of the Claremont Colleges

!  For further information, contact: Prof. Art Lee 216 Adams Hall [email protected] http://www.cmc.edu/math/CS/

Math undergraduate research

at CMC

Sam NelsonDepartment of Mathematical Sciences


August 31, 2012

1

Undergraduate Research in Mathematics

Mathematics today is a very active discipline, with thousands ofpapers published every year containing new theorems andresults. Research in pure and applied mathematics involves

proving new theorems

solving previously unsolved problems

creating and analyzing new mathematical models to betterunderstand and predict phenomena

Sam Nelson Orientation




















CMC Mathematicians are very active researchers, withpublications numbering in the hundreds and more always in theworks. Opportunities for CMC students to work collaborativelywith faculty in mathematical research include

Fletcher Jones Fellowships

Other summer research internships at CMC

Senior Thesis projects

Research for course credit































Undergraduate research in mathematics at CMC has manybenefits, which can include

Contributing to overall human knowledge, the thrill ofdiscovery

Your name associated with new mathematics for posterity

Summer pay, course credit

Opportunities to speak at conferences

Advantages when applying for graduate school and jobs










































Documents

Mathematical Sciences Information Session · Applied Mathematics Using mathematical tools to solve practical problems. Science Business Industry Mark Huber, CMC Mathematics at CMC