• 2022 Interdisciplinary Competition in Modeling (ICM) Results

    Congratulations to Radu Balan and to the UMD Math Modeling teams. The teams participated in the 2022 Interdisciplinary Competition in Modeling (ICM). This year 12100 teams participated in the ICM competition. The results of our two teams are: Team 2228337 (Sally Zhao, Naveen Raman, Clarissa Xia) has been awarded a Honorable Mention for Problem Read More
  • Joan Jian-Jian Ren Named as a Fellow of the IMS

    We are pleased to inform you that Joan Jian-Jian Ren was named as a Fellow of the IMS (Institute of Mathematical Statistics). Joan Jian-Jian Ren, Professor, University of Maryland - College Park, has been named Fellow of the Institute of Mathematical Statistics (IMS). Dr. Ren received the award for innovative and Read More
  • George Li named 2022 Goldwater Scholar

    Three University of Maryland undergraduates with strong records of published research have been awarded 2022 scholarships by the Barry Goldwater Scholarship and Excellence in Education Foundation, which encourages students to pursue advanced study and research careers in the sciences, engineering and mathematics. Patrick Kim, a junior physics and electrical engineering Read More
  • Bianca Viray receives 2022-2023 Birman Fellowship

    Bianca Viray, a professor at the University of Washington (UMD 2005), has been awarded the AMS Joan and Joseph Birman Fellowship for Women Scholars for the 2022–2023 academic year. The fellowship gives exceptionally talented women extra research support during their mid-career years. The primary selection criterion is the excellence of Read More
  • Congratulations to the Math Putnam Team

    Congratulations to the team under the leadership of Roohollah Ebrahimian. Our Putnam Team was ranked 20th out of 427 institutions this year. This is our fifth year in a row that we rank among top 20 teams in the Putnam competition. Our team members were Steppan Konoplev, Thomas Luo, and 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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