• In memory of our colleague David C. Lay

    Our long-time colleague Professor Eneritus David Lay passed away October 12, 2018. David earned his BA at Aurora College in 1962, and his PhD at UCLA in 1966. He then came to Maryland where he rose through the ranks to Professor in 1977. A gifted teacher, he won the campus Read More
  • Brin E-Nnovate Chaired Professor Michael Rapoport Colloquium talk in September

    Brin E-Nnovate Chaired Professor Michael Rapoport will deliver a Colloquium talk on September 26: "Scholze's Fields Medal''. Michael Rapoport is the former adviser of Peter Scholze and will share his insights on the personality and remarkable mathematical results of his former student. Read More
  • The Canadian Journal of Statistics Award 2018, to Victor de Oliveira and Benjamin Kedem

    The Canadian Journal of Statistics Award is presented each year by the Statistical Society of Canada to the author(s) of an article published in the journal, in recognition of the outstanding quality of the methodological innovation and presentation. This year’s winner is the article entitled “Bayesian analysis of a density ratio Read More
  • 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
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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