## Required Coursework

Applicants to the UW Bothell Secondary and Middle Level Teacher Certification M.Ed. who plan to earn an endorsement in Mathematics must have completed coursework in the following areas prior to starting the fieldwork portion of the program. Courses must have been completed with a minimum grade of 2.5.

Please note: it is not necessary to have completed an entire course in the content area. One course may cover multiple content areas if content was addressed in depth.

The following list contains examples of course content that meet the requirements for each subject area. Applicants may have completed the approved courses or courses with equivalent content.

### Calculus – 3 quarter courses or 2 semester courses

Examples of course title and content:

- Calculus 1: First quarter in calculus of functions of a single variable. Emphasizes differential calculus. Emphasizes applications and problem solving using the tools of calculus.
*(UW course number MATH 124, UWB course number B CUSP 124, Washington State Community College Common Course Number MATH 151)* - Calculus 2: Second quarter in the calculus of functions of a single variable. Emphasizes integral calculus. Emphasizes applications and problem solving using the tools of calculus.
*(UW course number MATH 125, UWB course number B CUSP 125, Washington State Community College Common Course Number MATH 152)* - Calculus 3: Third quarter in calculus sequence. Introduction to Taylor polynomials and Taylor series, vector geometry in three dimensions, introduction to multivariable differential calculus, double integrals in Cartesian and polar coordinates.
*(UW course number MATH 126, UWB course number B CUSP 126, Washington State Community College Common Course Number MATH 153)*

### Logic and Problem Solving – 1 course (100 level or above)

Examples of course title and content:

- Intro to Logic: Elementary symbolic logic; The development, application, and theoretical properties of an artificial symbolic language designed to provide a clear representation of the logical structure of deductive arguments.
*(UW course number PHIL 120, Washington State Community College Common Course Number PHIL 120)*

*If students take both MATH 444 and 445 at UW Seattle, MATH 444 can satisfy the Logic and Problem Solving course requirement

### Geometry – 1 course (200 level or above)

Examples of course title and content:

- Intro to Proofs: Introduce different methods for constructing simple proofs, including forwards/backwards proofs, contradiction, contraposition, and induction. The students will apply these methods to a variety of areas of mathematics, including simple number theory, relations, calculus concepts, and a study of infinity.
- Differential Geometry: Curves in 3-space, continuity and differentiability in 3-space, surfaces, tangent planes, first fundamental form, area, orientation, the Gauss Map
*.(Ex: MATH 442 at UW Seattle)* - Special Topics in Geometry: Content selected from such topics as homotopy theory, topological surfaces, advanced differential geometry, projective geometry, hyperbolic geometry, spherical geometry, and combinatorial geometry.
*(Ex: MATH 443 at UW Seattle)*

### Algebra – 2 courses (1 course must be 200 level or above)

Examples of course title and content:

- Basic properties of functions, graphs; with emphasis on linear, quadratic, trigonometric, exponential functions and their inverses. Emphasis on multi-step problem solving.
*(UW course number MATH 120, UWB course number B CUSP 123, Washington State Community College Common Course Number MATH 141 AND MATH 142)* - Intro to Differential Equations: Introduces ordinary differential equations. Includes first-and second-order equations and Laplace transform.
*(UW course number MATH 307, UWB course number STMATH 307)* - Linear and/or Matrix Algebra: Systems of linear equations, vector spaces, matrices, subspaces, orthogonality, least squares, eigenvalues, eigenvectors, applications. For students in engineering, mathematics, and the sciences.
*(UW course number MATH 308/318, UWB course number STMATH 308)*

### Statistics – 2 courses in Statistics OR 1 course in Calculus-based Statistics/Probability

Examples of course title and content:

- Statistical Methods: Elementary concepts of probability and sampling; binomial and normal distributions. Basic concepts of hypothesis testing, estimation, and confidence intervals; t-tests and chi-square tests. Linear regression theory and the analysis of variance.
*(UW course number STAT 311, UWB course number B BUS 215 and BIS 315 Washington State Community College Common Course Number MATH 146)* - Concepts of probability and statistics. Conditional probability, independence, random variables, distribution functions. Descriptive statistics, transformations, sampling errors, confidence intervals, least squares and maximum likelihood. Exploratory data analysis and interactive computing.
*(UW course number STAT 390)*

### Discrete Mathematics – 1 course (200 level or above)

Examples of course title and content:

- Computer Programming: Basic programming-in-the-small abilities and concepts including procedural programming (methods, parameters, return values), basic control structures (sequence, if/else, for loop, while loop), file processing, arrays and an introduction to defining objects.
*(UW course number CSE 142)*

### History/Foundations of Math – 1 course (300 level or above)

Examples of course title and content:

- History of Math: Survey of the development of mathematics from its earliest beginnings through the first half of the twentieth century.
*(UW course number MATH 420, UWB Special Topics)*