• 2024 Putnam Results

    We are very excited to report that our MAryland Putnam team ranked 7th among 477 institutions that participated in the 2024 Putnam math competition. Our team members this year were Daniel Yuan, Isaac Mammel, and Clarence Lam. Daniel Yuan ranked 26th among 3,988 participants. Clarence Lam and Isaac Mammel were recognized for… Read More

  • From Math Olympiads to Diplomacy: Meet Visiting Math Professor Qendrim Gashi

    Maryland Global, published a great interview with our visiting professor (and diplomat), Qendrim Gashi. The interview is available at https://marylandglobal.umd.edu/about/news/math-olympiads-diplomacy-meet-visiting-math-professor-qendrim-gashi Read More

  • Eugenia Brin, Longtime Supporter of Science and Performing Arts at UMD, Dies

    Eugenia Brin, a Russian immigrant and retired NASA scientist who, with her family of accomplished Terps, became an important benefactor of the University of Maryland, died on Dec. 3, 2024. She was 76 years old. The rest of the article can be read here: https://cmns.umd.edu/news-events/news/eugenia-brin-1948-2024 Read More

  • 2024 Michael Brin Dynamical Systems Prize for Young Mathematicians Awardees

    Math is excited to announce that Francisco Arana-Herrera has been awarded the 5th Michael Brin Dynamical Systems Prize for Young Mathematicians.  The prize was shared between Francisco and Rohil Prasad. Details about eh prize and previous winners can be found at  https://science.psu.edu/math/research/dynsys/dynamical-systems-prize-young-mathematicians Read More

  • UMD Launches Award to Recognize Dual Majors in Computer Science and Mathematics

    Starting Spring 2025, the Grant Family Outstanding Achievement Undergraduate Student Award will recognize graduating seniors excelling in both fields. Link to the article can be read here: https://www.cs.umd.edu/article/2024/11/umd-launches-award-recognize-dual-majors-computer-science-and-mathematics Read More
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Description

MATH 115 is a preparation for Calculus, either MATH 220 (for which Math 113 is an alternate prerequisite) or MATH 140, with a focus on functions and graphs and algebraic techniques preparatory to calculus. The functions studied include polynomials, rational functions, exponential and logarithmic functions, and trigonometric functions.

(A graphing calculator such as the TI- 83, is required for Math 115. It is used in exploring the graphs of functions and equations and in solving problems.)

Prerequisites

Satisfactory score on Math Department placement exam, completion of the appropriate module of MATH 003, or completion of Math 113.

Topics

Algebra

Inequalities
Absolute value inequalities
Table of signs for polynomial and rational inequalities

Functions

Domain
Operations including compositions
Inverses
Graphs
Symmetry
Transformations: Shifts, reflections, stretching and shrinking

Quadratic functions and equations

Applications involving quadratic equations
Parabolas
Extreme value problems
Quadratic related equations including radical equations

Polynomials

Shape of graph
Writing polynomial functions with specific properties
Using a graphing calculator to draw complete graphs

Rational functions

Finding intercepts and asymptotes
Graphing with and without calculator

Conic sections

Standard equations for parabolas, circles, ellipses, and hyperbolas, shifts of conic sections
(if time allows)

Exponential and Logarithmic functions

Definition
Graphs
Exponent rules
Laws of logarithms
Exponential and logarithmic equations
Exponential growth and decay

Trigonometry

Angles
Radian and degree measurement of angles
Arc length and angular speed

Trigonometric functions

Circle, point, and right-triangle definitions of functions
Graphs of trig functions
Sinusoidal graphs

Solving triangles

Right triangles
Law of Cosines
Law of Sines

Trigonometric identities

Reciprocal identities
Pythagorean identities
Negative-angle identities
Periodicity identities
Sine and cosine addition and subtraction identities
Double-angle identities
Power-reducing identities

Trigonometric equations

Finding algebraic solutions
Finding calculator solutions

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