• Outstanding Director of Graduate Studies Award

    Professor Konstantina Trivisa has been selected for the Outstanding Director of Graduate Studies (DGS) Award for 2018.  Directors of Graduate Studies are critical partners of the Graduate School in shaping graduate education and ensuring the success of graduate students.  The Outstanding Director of Graduate Studies Award recognizes exceptional contributions made Read More
  • Congratulations to Putnam Exam Participants

    Congratulations to our Putnam Exam participants. The University of Maryland Putnam Team was ranked 15th among the 575 competing institutions in the highly competitive Putnam mathematics exam on December 2, 2017. Congratulations to Aaron George, who ranked 39th and Erik Metz who ranked 81st, and to Jason Zou, Justin Hontz Read More
  • Girls Talk Math

    Girls Talk Math is a two-week summer day camp hosted by the Department of Mathematics at the University of Maryland. The camp will occur weekdays July 9-20, 2018 from 9:00 am - 4:00 pm. Rising-9th to rising-12th grade students who attend high school within driving distance of the University can apply. Read More
  • James Owings and Adam Kleppner

    The mathematics department mourns the recent passing of two of our Professors Emerti: Jim Owings and Adam Kleppner. James Claggett Owings, Jr. received his PhD in recursion theory at Cornell in 1966, under the direction of Gerald Sacks.  For many years, Jim was one of the leaders of the Maryland Read More
  • Upcoming Conferences

    We would like to draw your attention to several exciting conferences coming up in the Mathematics Department: February Fourier Talks - Thursday, February 15 - Friday, February 16, 2018 Geometry Week - Monday, March 12 - Friday, March 16, 2018 Spring Dynamics Conference - Wednesday, April 4 - Sunday, April 8, 2018 Read More
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Description

To develop the students' ability to construct a rigorous proof of a mathematical claim. Students will also be made aware of mathematical results that are of interest to those wishing to analyze a particular mathematical model. Topics will be drawn from logic, set theory, structure of the number line, functions, sequences and continuity.

Credit will be granted for only one of the following: MATH 310 or MATH 307.
Math majors may not use this course for one of their upper level mathematics requirements.

Prerequisites

Math141 is a prerequisite. Math241 and Math240/461 (or Math340 and 341) are pre/co-requisites. 

Topics

Introduction to Sets

Set operations
De Morgan's Law

Some Logic

Direct proofs
Contrapositive proofs
Proofs by contradiction
Quantifiers
Impact of change of quantifiers, order of quantifiers and negations on meaning of statements
Disproving statements

Proof techniques applied to:

Divisibility
Real number properties
Set equalities
Equivalence relations

Cardinality

Size of sets
Countability
Bernstein's Theorem

Induction

First principal of finite mathematical induction
Second principal of finite mathematical induction
Applications

Sequences

Definition of limit
Convergence
Monotone convergence theorem
Bolzano-Weierstrass theorem

Completeness

Greatest lower bounds
Least upper bounds
Cauchy sequece

Functions

Injective, Surjective and Bijective functions
Continuous functions with sequence definition
Continuous functions with epsilon/delta definition

  • William E. Kirwan Hall, home of the Mathematics Department

    William E. Kirwan Hall, home of the Mathematics Department

  • The Experimental Geometry Lab explores the structure of low dimensional space

    The Experimental Geometry Lab explores the structure of low dimensional space

  • Maryland mathematicians help to investigate the inner workings of E_8

    Maryland mathematicians help to investigate the inner workings of E_8

  • Hyperbolic Space Tiled with Dodecahedra

    Hyperbolic Space Tiled with Dodecahedra

  • Isotropoic Gaussian random field with Matern correlation

    Isotropoic Gaussian random field with Matern correlation

  • Part of the proof of the Peter-Weyl theorem

    Part of the proof of the Peter-Weyl theorem