• Two Math Faculty to Speak at ICM

    Congratulations to faculty members Pierre-Emmanuel Jabin and Xuhua He who have been selected as invited speakers at the International Congress of Mathematics in Rio de Read More
  • Promotions and New Faculty

    We are delighted to announce that faculty members Jacob Bedrossian, Maria Cameron, Amin Gholampour, and Christian Zickert have been promoted to the rank of Associate Read More
  • William E. Kirwan Distinguished Undergraduate Lectures

    Mathematics for Art Investigation: Mathematical tools for image analysis increasingly play a role in helping art historians and art conservators assess the state of conversation Read More
  • Upcoming Conferences

    We would like to draw your attention to several exciting conferences coming up in the Mathematics Department: The Spring Dynamics Conference, Friday, March 31 - Sunday, Read More
  • Putnam Exam

    We would like to congratulate the University Maryland team on their excellent performance on this year's William Lowell Putnam Mathematical Competition, the premier undergraduate math 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