• Archana Receives the Donna B. Hamilton Award

    Archana Khurana has been selected to receive the Donna B. Hamilton Award for Excellence in Undergraduate Teaching in a General Education Course.  Awards are based solely on student nominations and are solicited from across campus.  From the many nominations received, the selection committee was very impressed by the student experience… Read More

  • Yanir Receives a Do Good Campus Fund Grant

    Yanir’s proposal on “Incorporating outreach into the curriculum via experiential learning” is one of the only 27 projects out of 140 submissions that were funded by the UMD Do Good Campus Fund. Read More

  • Congrats to 3 CMNS Students Named Goldwater Scholars

    Congratulations to UMD’s 3 Goldwater Scholars this year, all from CMNS: Junior physics and mathematics double-degree student Yash Anand Sophomore atmospheric and oceanic science and physics double-degree student Malcolm Maas Junior biological sciences and mathematics double-degree student Jerry Shen Over the last 15 years, UMD’s nominations yielded 49 scholarships—No. 2… Read More

  • Maria Cameron Receives the 2024 MURI Award

    Congratulations to Maria Cameron for her MURI award. MURI are multidisciplinary university research initiative grants that are awarded by the department of defense. Cameron’s grant is sponsored by the office of naval research. Her team includes Balakumar Balachandran (ME) and Miao Yu (ME). This is a project on “disorder-influenced collective… Read More

  • A $27.2M Gift to the Math Department by the Brin Family

    The university announced today a big gift to the Math Department. The very generous gift of $27.2M was made by Michael & Eugenia Brin. The gift will endow the Brin Mathematics Research Center, establish an endowed chair, and launch a summer camp for high school students. The official university’s press… 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 principle of finite mathematical induction
Second principle 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

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