# Mathematics major

## Faculty Adviser

**Robert Hauss: **503-491-7383 | Room AC2576 | Robert.Hauss@mhcc.edu

**David Favreault: **503-491-7608 | Room AC2572 | David.Favreault@mhcc.edu

The math taught at Mt. Hood Community College focuses on using math in real life. This includes problem solving, technology use and understanding concepts. Many career choices require math. We welcome majors entering at all math levels. To learn more, please contact a math instructor.

Curricular Outcomes

At the completion of this curriculum, students should be able to:

- Effectively communicate a problem-solving process, results and conclusions using mathematical terminology and correct mathematical syntax
- Apply mathematical concepts, skills, reasoning and modeling to solve problems arising from the real world
- Model problem situations visually, numerically, graphically and/or algebraically and make connections among various models
- Demonstrate a command of functions from multiple perspectives
- Determine if a solution is reasonable, verify results and compare solutions from different approaches
- Use appropriate technology to analyze and solve mathematical problems
- Describe and interpret, from multiple perspectives, the purpose and usefulness of the derivative concept
- Describe and interpret, from multiple perspectives, the purpose and usefulness of the integral concept

See an adviser to personalize this plan and/or to create a plan that starts with the math sequence before calculus. It is possible to start the calculus sequence as late as spring of the first year, take summer classes, and finish by spring of the following year. Students hoping to teach at any level are strongly encouraged to apply for work as a tutor in the Learning Success Center for hands-on experience.

Students interested in pursuing the Mathematics major can complete the following courses toward the Math and Science requirements and/or electives on the AS (recommended), AAOT, ASOT-B, AGS or ASLA degrees. Students are highly encouraged to work with a university transfer adviser to ensure transferability of courses. Admitted students may also log on to Navigate to start the process of building an academic plan based on this major and can notify an adviser for review.

Code | Title | Credits |
---|---|---|

MTH251 | Calculus I: Differential Calculus | 5 |

MTH252 | Calculus II: Integral Calculus | 5 |

MTH253 | Calculus III | 4 |

MTH254 | Calculus IV: Vector Calculus | 5 |

MTH255 | Calculus V: Multivariable/Vector Calculus Part 2 | 4 |

MTH256 | Differential Equations | 5 |

MTH261 | Linear Algebra | 4 |

STAT243Z | Elementary Statistics I (Course offered online) | 4 |

STAT244 | Elementary Statistics II | 4 |

## Transfer Schools

Exploring **mathematics **as your major? Learn more with MHCC's Career Coach, which covers: skills needed for each career, wages, employment rates, and live job postings in the Greater Multnomah County Area.

Careers related to mathematics:

The following shows just one example of how students can complete an Associate of Science degree while also taking lower-division history courses. Be sure to work with an MHCC adviser and the transfer institution you'd like to attend to ensure correct courses are being taken. Not all courses are offered every term. Click on a course number to see what term(s) the course is typically offered.

**Full time**= 12 or more credits per term; takes about 2 years to complete.**3/4 time**= 9 to 11 credits per term; takes about 3 years to complete.**Part time**= 6 to 8 credits per term; takes about 4 years to complete.

## Sample Plan (full time)

First Quarter | Credits | |
---|---|---|

MTH251 | Calculus I: Differential Calculus | 5 |

WR121Z | Composition I (Course offered online) | 4 |

Health & Physical Education | 3 | |

Elective / university requirement | 3 | |

Credits | 15 | |

Second Quarter | ||

MTH252 | Calculus II: Integral Calculus | 5 |

STAT243Z | Elementary Statistics I (Course offered online) | 4 |

WR122Z | Composition II (Course offered online) | 4 |

Credits | 13 | |

Third Quarter | ||

MTH261 | Linear Algebra | 4 |

STAT244 | Elementary Statistics II | 4 |

Oral Communication | 3-4 | |

Social Science | 3-4 | |

Credits | 16 | |

Fourth Quarter | ||

MTH254 | Calculus IV: Multivariable/ Vector Calculus Part 1 | 5 |

Arts & Letters | 3-4 | |

Elective / university requirement (PH211 recommended) | 5 | |

Credits | 13-14 | |

Fifth Quarter | ||

MTH255 | Calculus V: Multivariable/Vector Calculus Part 2 | 4 |

MTH253 | Calculus III | 4 |

Arts & Letters | 3-4 | |

Elective / university requirement (PH212 recommended) | 5 | |

Credits | 16-17 | |

Sixth Quarter | ||

MTH256 | Differential Equations | 5 |

MTH275 | A Bridge to Upper-Division Mathematics | 3 |

Social Science | 3-4 | |

Elective / university requirement (PH213 recommended) | 5 | |

Credits | 17 | |

Total Credits | 90-92 |

**MTH010 Conceptual Arithmetic **

Credits 4Summer/Fall/Winter/Spring

**Registration Requirement:** Students must be either concurrently enrolled in RD090 and WR090, or IECC201R and IECC201W, or place above those levels.

This course is for students who need to master the concepts of whole numbers, fractions or decimals. The emphasis of the course is on understanding concepts, estimation, simple measurement, language usage and reasoning skills. Real world applications are used and the reasonableness of answers is stressed. Calculator use is taught for computation. A scientific calculator with a fraction key, algebraic logic and expression playback is required. A specific model of calculator may be required.

### View Course Outcomes:

- Communicate effectively (orally and in writing) a problem solving process, results and conclusions using mathematical terminology and correct mathematical syntax
- Complete basic arithmetic calculations and comparisons mentally (including exponents, square roots, single-digit multiplication and operations with powers of ten)
- Complete basic fractions computations with appropriate models and real world applications (including reducing, equivalent, converting between improper and mixed number forms, adding, subtracting, multiplying and dividing)
- Compute answers to percent problems using common fraction equivalents and reasoning
- Convert among equivalent forms of fractions, decimals and percent
- Create and interpret fraction models, including: shaded figures, number lines, ruler readings, simple probabilities, fraction of a total and division
- Demonstrate an understanding of addition, subtraction, multiplication and division by choosing a correct operation or series of operations in an application context
- Determine if a solution is reasonable and verify results
- Estimate values of all calculations covered in this course
- Identify terms and factors in an expression and evaluate the expression showing steps
- Measure accurately using inches, centimeters and millimeters
- Model decimal numbers using place value, money, fractions and metric rulers
- Model percent using real situations and pictures
- Translate large numbers and decimals between word form and numerical form
- Use a calculator with one-step entry to simplify expressions, adding parentheses as needed
- Use and explain the base ten place value system, including rounding
- Use mathematical symbols to represent and answer questions about real situations, including addition, subtraction, multiplication, division, fractions, percent and money
- Without calculating, compare a fraction or numerical expression involving fractions to one-half, one and two and explain the relationship

**MTH020 Applied Arithmetic and Pre-algebra **

Credits 4Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH010; each with a grade of "C" or better; or placement above stated course levels. A scientific/graphing calculator with fraction output capabilities is required.

This course is intended for both the career-technical and baccalaureate-prep student. It includes the use of mathematics as a language, rational number operations, estimating and approximating, scientific notation, ratios, percents, proportions, the metric and U.S. Customary systems, formula development and evaluation and practical geometry. A scientific/graphing calculator with fraction output capabilities is required and its use is fully integrated in the course. A specific model of calculator may be required.

### View Course Outcomes:

- Determine if a solution is reasonable and verify results
- Communicate effectively (orally and in writing) a problem solving process, results and conclusions usingmathematical terminology and correct mathematical syntax
- Complete basic arithmetic calculations and comparisons mentally (including square roots, common fraction-decimal-percent equivalents, single-digit multiplication and operations with powers of ten)
- Complete basic fractions computations with explanations and/or pictures (including reducing, building, equivalent,fraction of, converting between improper and mixed number forms, adding, subtracting, multiplying and dividing)
- Compute exact answers to percent problems using technology
- Define, apply, estimate, and calculate perimeters and areas of rectangles, triangles, circles and compound figures,including appropriate units
- Determine (with explanations) the results of sums, differences, products, and quotients of positive & negativenumbers
- Determine which of two quantities (numerical expressions, measurements, fractions, ratios) is bigger conceptually(without calculating) and explain the choice by talking about the operation or the physical meaning
- Draw pictures and/or use fraction pieces to represent fractions and fraction arithmetic problems
- Estimate values (including one-step calculations, fractions, percents, square roots)
- Identify terms in an expression and evaluate the expression showing steps
- Measure accurately using inches and centimeter rulers
- Mentally compute exact answers to percent problems by moving the decimal (10%), halves (50%) and combinationsthereof
- Translate between and compute with large numbers given in word form, scientific notation or numerical form
- Use a calculator with one-step entry to simplify expressions, adding parentheses as needed
- Use mathematical symbols to represent and answer questions about real situations, like ratios, measurements,writing expressions, etc
- Use variables as abbreviations and include units everywhere to prepare for algebra

**MTH058 Quantitative Reasoning I **

Credits 6Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH020; each with a grade of "C" or better; or placement above stated course levels. Students need a calculator and computer access. Calculator needs MathPrint, fraction and editing capability.

Quantitative Reasoning I prepares students to use non-STEM mathematics to become contributing citizens, educated consumers and effective users of numerical information. Students gain number sense, build estimation skills and solve realistic problems. Students use reasoning, percents, proportions, and formulas. Technology, especially spreadsheets, is used as a problem-solving tool. Clear communication of processes using words, data and symbols is emphasized. This course prepares the student for MTH98 and then MTH105.

### View Course Outcomes:

- Create mathematical models to solve real world problems using formulas, graphs and numerical approaches.
- Find areas and perimeters using formulas and conceptually.
- Present an argument about quantitative ideas and support it with quantitative data.
- Solve and model real world problems involving proportionality.
- Solve quantitative problems using numerical skills mentally and with technology.
- Solve real world problems using mathematical concepts. (All topics in this course should be taught in context. Emphasis is not on symbolic mathematics but on interpretation and conceptual understanding.)
- Use mathematical symbols to model and solve real world problem situations.
- Use technology (calculators, spreadsheets, etc.) to represent and solve real world problems.
- Use units to communicate process, answers and as a problem solving tool.

**MTH060 Beginning Algebra I (Course offered online) **

Credits 4Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH020; each with a grade of "C" or better, or placement above stated course levels. A graphing calculator is required. A TI-83 Plus or TI-84 is recommended.

This is the first half of the beginning algebra course for both the baccalaureate-prep and career-technical student emphasizing problem-solving and practical applications using numerical, algebraic and graphical models. The topics covered include the real number system, positive integer exponents, unit conversions and dimensional analysis, simplifying algebraic expressions, modeling and solving problem situations with linear equations and formulas, the Cartesian plane and applications which require the Pythagorean Theorem. A graphing calculator is required and its use is fully integrated in the course.

### View Course Outcomes:

- Simplify and solve basic expressions and equations\\n[Objectives 1a - 1i]
- Model data verbally and with equations, graphs and tables of values\\n[Objectives 2a - 2f]
- Perform arithmetic arising from real-world applications\\n[Objectives 3a - 3f]
- Use units to solve problems and communicate effectively\\n[Objectives 4a - 4c]
- Communicate effectively (in writing) a problem-solving process, results, and conclusions using mathematical terminology and correct mathematical syntax\\n[Objectives 5a - 5g]
- Use technology to display data and solve problems\\n[Objectives 6a - 6d]

**MTH065 Beginning Algebra II (Course offered online) **

Credits 4Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH060; each with a grade of "C" or better, or placement above stated course levels. A graphing calculator is required. A TI-83 Plus or TI-84 is recommended.

This is the second half of the beginning algebra course for both the baccalaureate-prep and career-technical student emphasizing problem-solving and practical applications using numerical, algebraic and graphical models. The topics covered include graphs and equations of lines, negative integer exponents, solving formulas and rational equations and practical geometry. A graphing calculator is required and its use is fully integrated in the course.

### View Course Outcomes:

- Measure and draw figures from 2D geometry\\n[Objectives 1a - 1e]
- Use geometric vocabulary and notation for 2D figures and 3D solids\\n[Objectives 2a - 2d]
- Solve problems involving 3D geometric solids\\n[Objectives 3a - 3e]
- Apply properties of polygons, similar figures and congruent angles in 2D geometry\\n[Objectives 4a - 4f]
- Identify, describe and model linear relationships\\n[Objectives 5a - 5g]
- Outcome 6 - Simplify expressions and solve equations using the lowest common denominator, common factoring and products of multi-term expressions\\n[Objectives 6a - 6f]
- Outcome 7 - Use properties of positive and negative integer exponents\\n[Objectives 7a - 7c]

**MTH084 Applied Trigonometry with Modeling **

Credit 1Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH065; each with a grade of "C" or better, or placement above stated course levels.

This is an introductory course in applied trigonometry. Topics covered include right triangle trigonometry and an introduction to models of compound interest. Practical applications are emphasized.

### View Course Outcomes:

- Apply right triangle trigonometry to determine vertical and horizontal displacement and slant distance between two points on the Cartesian plane
- Convert between decimal degree angle measure and degrees, minutes and seconds
- Determine all unknown sides and angles of right triangles using trigonometry
- Model constant percentage rate growth using exponential functions
- Sketch diagrams from written descriptions
- Use diagrams to solve applications including those that involve percent slope

**MTH095 Intermediate Algebra with Right Triangle Trigonometry (Course offered online) **

Credits 5Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH065; each with a grade of "C" or better, or placement above stated course levels. A graphing calculator is required; TI-83 Plus or TI-84 is recommended.

This is an interactive, technology-based course, which investigates the connections and interplay among various mathematical topics for both the baccalaureate-prep and technical-prep student. The function concept is introduced informally. Linear and quadratic functions and their graphs are covered in-depth. Other topics include rational exponents, radical and rational equations, linear and non-linear systems and right triangle trigonometry. A heuristic approach to problem-solving is emphasized with problem situations modeled numerically, algebraically and graphically.

### View Course Outcomes:

- Absolute Value Functions: Demonstrate a basic understanding of absolute value functions of the form y = |mx +b|. See objectives #25-28.
- Exponential Functions: Solve real-life percent problems and exponential equations numerically and graphically. See objectives #22-24.
- Functions and Modeling: Demonstrate a basic understanding of the function concept, and model applied problems and patterns numerically, graphically, and algebraically. See objectives #6-11.
- Linear Functions: Demonstrate a comprehensive understanding of linear functions and systems, and use linear information given in numerical, graphical or algebraic form. See objectives #12-21.
- Overarching: Effectively communicate mathematics using appropriate mathematical terminology and correct mathematical synta,X model and solve problems using a variety of methods, judge the reasonableness of and verify solutions, and maintain and strengthen prerequisites. See objectives #1-5.
- Quadratic Functions: Demonstrate a comprehensive understanding of quadratic functions. See objectives #29-41.
- Rational Exponents: Demonstrate an understanding of rational exponents, and simplify expressions and solve equations that involve rational exponents. See objectives #42-46.
- Right Triangle Trigonometry: Demonstrate a basic understanding of right triangle trigonometry and how and when to apply it in real-world situations. See objectives #47-50.

**MTH098 Quantitative Reasoning II **

Credits 4Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH058; each with a grade of "C" or better, or placement above stated course levels. Students need a calculator and computer access. Calculator needs MathPrint, fraction and editing capability.

Quantitative Reasoning II prepares students to use non-STEM mathematics to become contributing citizens, educated consumers and effective users of numerical information. Students develop critical thinking skills and solve realistic problems. Students use iterative processes, advanced percents, linear and exponential functions, and data in mathematical modeling. Technology, especially spreadsheets, is used as a problem-solving tool. Clear communication of processes using words, data and symbols is emphasized. This course prepares the student for MTH105.

### View Course Outcomes:

- Linear & Exponential Models: Compare and contrast linear and exponential functions.
- Linear & Exponential Models: Create and use linear models as a problem-solving tool.
- Linear & Exponential Models: Determine if a situation is exponential by investigating relative change in the given model (numeric, graph, algebraic, and in context).
- Linear & Exponential Models: Determine if a situation is linear by investigating constant rate of change in the given model (numeric, graph, algebraic, and in context).
- Linear & Exponential Models: Determine slope as a ratio and interpret in context using units of input and output.
- Linear & Exponential Models: Determine the slope in linear contexts.
- Linear & Exponential Models: Identify whether a growth or decay model shows additive growth, exponential (multiplicative) growth or neither of the above, using tables, graphs, written descriptions, spreadsheets and equations.
- Linear & Exponential Models: Interpret the meaning of input/output pairs, including horizontal and vertical intercepts, in the context of real-world situations.
- Linear & Exponential Models: Write an exponential equation, given relative change and initial value. Given an exponential equation, determine the relative change and initial value.
- Linear & Exponential Models: Write the equation of a line, given slope and intercept. Given the equation of a line, determine the slope and intercept.
- Modeling / Problem-Solving: Create appropriate visual representations of quantitative information using technology, including bar charts and pie charts starting with categorical counts/percentages (not raw data).
- Modeling / Problem-Solving: Create input/output graphs using technology.
- Modeling / Problem-Solving: Identify how choices such as scale and dimension can be used in visual representations to highlight specific attributes of quantitative information.
- Modeling / Problem-Solving: Interpret visual representations of quantitative information, including input/output graphs on the Cartesian plane, bar charts, and pie charts.
- Modeling / Problem-Solving: Model linear and exponential functions numerically, graphically, algebraically, and in context (both explicitly and iteratively).
- Modeling / Problem-Solving: Solve linear and exponential equations graphically.
- Modeling / Problem-Solving: Solve problems using multiple representations of data models, including tables, graphs, algebraic expressions, pictures and spreadsheets.
- Modeling / Problem-Solving: Solve relationships by extending a numerical pattern.
- Numeracy: Compare the relative magnitudes of small/large numbers.
- Numeracy: Estimate in context.
- Numeracy: Interpret and use large and small numbers written in word form or scientific notation.
- Overarching objectives: All topics in this course should be taught in context. Emphasis is not on symbolic mathematics but on interpretation and intuitive understanding.
- Overarching objectives: Apply mathematical concepts to real-world situations.
- Overarching objectives: Create and use visual tools such as sketches, fraction/percent pictures and graphs to solve problems.
- Overarching objectives: Demonstrate clear, coherent communication of process, reasoning, and answers. (If a student chooses to use mathematical symbols, the notation must be correct.)
- Overarching objectives: Determine and justify if a solution is reasonable.
- Overarching objectives: Solve practical problems using various strategies. Make decisions about each problem situation: how to approach the problem/strategy, with/without technology, which technology, should the answer be exact or approximate, rounding results reasonably.
- Overarching objectives: Use prerequisite skills, especially percents, using and creating graphs and tables in varied situations, using units appropriately, solving two-step equations.
- Percents: Analyze a situation and determine what number is the base/reference value to which the percent is applied.
- Percents: Calculate and interpret results in situations requiring successive percents.
- Percents: Interpret and calculate a percent increase or decrease as a comparison to 100%. (e.g. 1.04 or 0.96 )
- Symbolic manipulation: Simplify algebraic expressions used in applications at this level.
- Symbolic manipulation: Solve (algebraically) and check linear equations in one variable used in applications at this level.
- Technology / Spreadsheets: Copy and paste charts and data between and within spreadsheet and word processor software.
- Technology / Spreadsheets: Use spreadsheets to compute with iterative processes.
- Technology / Spreadsheets: Use tables and graphs in electronic documents to present coherent solutions to problems involving quantitative data.
- Units: Predict units of an answer based on a situation and/or formula.
- Units: Solve proportional relationships using dimensional analysis techniques.
- Units: Use dimensional analysis as a problem-solving technique in many contexts.

**MTH105Z Math in Society **

Credits 4Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH095 or MTH098; each with a grade of "C" or better; or placement above stated course levels.

An exploration of present-day applications of mathematics focused on developing numeracy. Major topics include quantitative reasoning and problem-solving strategies, probability and statistics, and financial mathematics; these topics are to be weighted approximately equally. This course emphasizes mathematical literacy and communication, relevant everyday applications, and the appropriate use of current technology.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- State-wide outcome 1 - Employ mathematical reasoning skills when reading complex problems requiring quantitative or symbolic analysis and demonstrate versatility in the consideration and selection of solution strategies.
- State-wide outcome 2 - Demonstrate proficiency in the use of mathematical symbols, techniques, and computation that contribute to the exploration of applications of mathematics.
- State-wide outcome 3 - Use appropriate mathematical structures and processes to make decisions and solve problems in the contexts of logical reasoning, probability, data, statistics, and financial mathematics.
- State-wide outcome 4 - Use appropriate representations and language to effectively communicate and interpret quantitative results and mathematical processes orally and in writing.
- State-wide outcome 5 - Demonstrate mathematical habits of mind by determining the reasonableness and implications of mathematical methods, solutions, and approximations in context.

**MTH111Z Precalculus I: Functions (Course offered online) **

Credits 4Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH095; each with a grade of "C" or better; or placement above stated course levels.

A course primarily designed for students preparing for trigonometry or calculus. This course focuses on functions and their properties, including polynomial, rational, exponential, logarithmic, piecewise-defined, and inverse functions. These topics will be explored symbolically, numerically, and graphically in real-life applications and interpreted in context. This course emphasizes skill building, problem solving, modeling, reasoning, communication, connections with other disciplines, and the appropriate use of present-day technology.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- State-wide outcome 1- Explore the concept of a function numerically, symbolically, verbally, and graphically and identify properties of functions both with and without technology.
- State-wide outcome 2- Analyze polynomial, rational, exponential, and logarithmic functions, as well as piecewise-defined functions, in both algebraic and graphical contexts, and solve equations involving these function types.
- State-wide outcome 3- Demonstrate algebraic and graphical competence in the use and application of functions including notation, evaluation, domain/range, algebraic operations & composition, inverses, transformations, symmetry, rate of change, extrema, intercepts, asymptotes, and other behavior.
- State-wide outcome 4- Use variables and functions to represent unknown quantities, create models, find solutions, and communicate an interpretation of the results.
- State-wide outcome 5- Determine the reasonableness and implications of mathematical methods, solutions, and approximations in context.

**MTH112Z Precalculus II: Trigonometry **

Credits 4Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH111/MTH111Z; each with a grade of "C" or better; or placement above stated course levels.

A course primarily designed for students preparing for calculus and related disciplines. This course explores trigonometric functions and their applications as well as the language and measurement of angles, triangles, circles, and vectors. These topics will be explored symbolically, numerically, and graphically in real-life applications and interpreted in context. This course emphasizes skill building, problem solving, modeling, reasoning, communication, connections with other disciplines, and the appropriate use of present-day technology.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- State-wide outcome 1 - Translate among various systems of measure for angles including radians, degrees, and revolutions.
- State-wide outcome 2 - Represent, manipulate, and evaluate trigonometric expressions in terms of sides of a right triangle and in terms of the coordinates of a unit circle.
- State-wide outcome 3 - Graph, transform, and analyze trigonometric functions using amplitude, shifts, symmetry, and periodicity.
- State-wide outcome 4 - Manipulate trigonometric expressions and prove trigonometric identities.
- State-wide outcome 5 - Solve trigonometric equations using inverses, periodicity, and identities.
- State-wide outcome 6 - Define, represent, and operate with vectors both geometrically and algebraically.
- State-wide outcome 7 - Apply the law of sines and the law of cosines to determine lengths and angles.
- State-wide outcome 8 - Use variables, trigonometric functions, and vectors to represent quantities, create models, find solutions, and communicate an interpretation of the results.
- State-wide outcome 9 - Determine the reasonableness and implications of mathematical methods, solutions, and approximations in context.

**MTH211 Fundamentals of Elementary Mathematics I **

Credits 4Fall

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH095; each with a grade of "C" or better; or placement above stated course levels. A scientific calculator with a fraction key is required.

This course is part one of mathematics for future K-8 teachers. The course includes problem-solving, functions, the structure of number systems, operations on whole numbers and number theory. Various concrete, pictorial and heuristic problem-solving strategies are used along with algorithmic problem-solving. A required computer component will reinforce the concepts of the course.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Define and model the four basic operations on whole numbers, and analyze the basic algorithms associated with each operation.
- Describe and perform operations on sets. Describe the usefulness of sets as problem solving tools.
- Describe the history of numeration and the underlying structure of our numeration system.
- Identify, describe and use fundamental concepts related to divisibility, factors, multiples, and prime numbers.
- Solve problems capably using multiple techniques. Model and interpret elementary mathematics.

**MTH212 Fundamentals of Elementary Mathematics II **

Credits 4Winter

**Registration Requirement:** MTH211 with a grade "C" or better, or instructor consent. A scientific calculator with a fraction key is required.

This course includes mathematics for future K-8 teachers. The course includes problem-solving, the structure of the integer, rational and real number systems, operations on integers, fractions and decimals, ratio and proportion, the meaning and use of percent and graphical statistics. Various concrete, pictorial and heuristic problem-solving strategies are used along with algorithmic problem-solving. A required computer component will reinforce the concepts of the course.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Communicate effectively, in writing and orally, a problem solving process to model and interpret elementary mathematics.
- Define integers, rational numbers, and decimals and model and perform algorithms for operations on each of these family of numbers.
- Define the meaning of percent, identify the equivalence among percents, decimals and fractions, and use percent in problem solving.
- Describe the meaning of ratios and proportions along with techniques for using ratios and proportions to represent and solve problems.

**MTH213 Fundamentals of Elementary Mathematics III **

Credits 4Spring

**Registration Requirement:** MTH212 with a grade of "C" or better; or instructor consent.

This course is mathematics for future K-8 teachers. Various concrete, pictorial and heuristic problem-solving strategies are used to explore geometry, measurement, probability and numerical statistics. The course includes two- and three-dimensional shapes and their properties, standard/nonstandard measurement basic probability and numerical statistics.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Communicate effectively, in writing and orally, a problem solving process to model and interpret elementary geometry concepts.
- Define and use probability and counting techniques related to computing probabilities of events.
- Define and use the concept of congruence and similarity.
- Define, identify, and categorize classifications and properties of two- and three- dimensional figures.
- Define, interpret, and use basic statistical concepts.
- Describe, recognize, and create various symmetries and techniques for tessellating the plane.
- Explain and use the basic ideas and formulas for measuring perimeter and area, surface area and volume.
- Measure and interpret lengths, areas, volumes, temperatures, and weights with basic systems used to measure.

**MTH251 Calculus I: Differential Calculus **

Credits 5Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH112; each with a grade of "C" or better, or placement above stated course levels. A CAS-capable graphing calculator is required.

Calculus I covers the concepts, computations and applications of differential calculus. Functions and derivatives will be modeled symbolically, numerically, graphically and in words. A CAS-capable graphing calculator is required.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Determine the limit of a function. [SLO: 1-4, 18]
- Identify the properties of continuity and determine if a function is continuous on an interval. [SLO: 5]
- Determine the derivative of a function. [SLO 6-10]
- Apply limits and derivatives in the context of real world problems. [SLO: 12-16]
- Demonstrate the appropriate use and understanding of mathematical notation. [SLO: 11, 17]

**MTH252 Calculus II: Integral Calculus **

Credits 5Summer/Fall/Winter/Spring

**Registration Requirement:** MTH251, with a grade of "C" or better.

Calculus II covers the concepts, computation and applications of integral calculus. Functions and integrals are modeled symbolically, numerically, graphically and in words. A CAS-capable graphing calculator is required.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Determine and interpret definite integrals (objectives 1-8)
- Determine and interpret antiderivatives (objectives 9-15)
- Determine and interpret improper integrals (objectives 18-19)
- Use integrals and antiderivatives to solve applied problems (objectives 16, 20-22)
- Summarize the main ideas and applications of integral calculus (objective 17)

**MTH253 Calculus III **

Credits 4Winter

**Registration Requirement:** MTH252, with a grade of "C" or better. A CAS-capable graphing calculator is required. A computer laboratory may be included.

This is the third course in the calculus sequence covering infinite sequences and series, and an introduction numerical methods in calculus with coding.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Answer applied/conceptual questions from Precalculus, Differential and Integral Calculus and Infinite Series, using numerical techniques. Compare these approximate solutions to exact solutions when exact solutions exist. [See Objectives #1-2]
- Communicate mathematics using appropriate mathematical terminology and correct mathematical synta,X model and solve problems using a variety of methods, judge the reasonableness of and verify solutions, maintain and strengthen prerequisites. [See objectives #1-5]
- Generate code to approximate Precalculus and Calculus mathematics. [See Objectives #1-2]
- Model and solve application problems with sequences and series (finite and infinite). [See Objectives #3-8]
- Support understanding of calculus concepts with technology (hand-held and/or computer as appropriate). [See Objectives #1-2]

**MTH254 Calculus IV: Multivariable/ Vector Calculus Part 1 **

Credits 5Fall

**Registration Requirement:** RD090, WR090 and MTH252, each with a grade of "C" or better. The CAS-capable calculator is required. A required computer component is included outside of class.

This course includes an introduction to multivariable functions, partial derivatives, and integration with multivariate functions. It also includes an introduction to vector calculus including dot and cross products, gradients and directional derivatives, optimization of multivariable functions, vector-valued functions including parametric curves in space and motion, vector fields, and applications.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Apply differential and integral calculus concepts to vectors and 3D objects described through various coordinate systems (polar, rectangular, cylindrical, or spherical) and 3D objects describing area and volume. [See Objective 29]
- Apply differential calculus concepts to multivariable functions. [See Objectives #13-16]
- Apply integral calculus concepts to multivariable functions. [See Objectives #17-20]
- Apply mathematical reasoning and modeling to solve problems arising from the real world. Mathematically model problem situations verbally, numerically, visually, graphically and/or algebraically. [See objective #1]
- Apply understanding and application of functions to a 3D setting (,Xy,z). [See Objectives #8-12]
- Communicate (orally and in writing) a problem solving process, results and conclusions using mathematical terminology and correct mathematical syntax.
- Determine if a solution is reasonable and verify results. Also, determine if answers are equivalent from the textbook, from the calculator, and answers developed by hand. [See Objectives #2-3]
- Identify connections among verbal, numeric, visual, graphical and algebraic models.
- Perform and apply vector computations (from both algebraic and geometric perspectives) including vector addition and subtraction, scalar multiplication, magnitude of a vector, unit vector in a given direction, vector components, dot product, cross product, gradients, directional derivatives, critical points, Lagrange, length of an arc, and curvature. [See Objectives #21-28]
- Support understanding of multivariable calculus concepts using technology (hand-held and/or computer as appropriate). [See Objectives #4-7]

**MTH255 Calculus V: Multivariable/Vector Calculus Part 2 **

Credits 4Winter

**Registration Requirement:** MTH254 with a grade of "C" or better. The CAS-capable calculator is required. A required computer component is included outside of class.

This course is a study of vector calculus including vector fields, line integrals, FTC, Green's Theorem, flux, divergence, curl and Stokes' Theorem. It also includes parametric curves and surfaces, as well as change of coordinates via the Jacobian. The CAS-capable calculator is required. A required computer component is included outside of class.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Apply calculus concepts to vector fields and line integrals. [Objectives 1-13]
- Apply calculus concepts to vector fields and surface integrals. [Objectives 14-21]
- Parametrize curves and surfaces in 3 dimensions. [Objectives 28-31]
- Summarize and apply the main theorems of vector calculus. [Objectives 22-27]

**MTH256 Differential Equations **

Credits 5Spring

**Registration Requirement:** MTH252 with a "C" or better.

This introductory course examines the application of ordinary differential equations as mathematical models for a variety of disciplines. Students explore analytical, graphical and numerical techniques for solving ordinary differential equations and systems of ordinary differential equations. A systems approach is used with relevant linear algebra concepts developed as needed. A CAS-capable graphing calculator is required.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Apply numerical methods to determine successive approximations to the solution of an initial value ODE or system ofODEs
- Assess the value and limitations of the existence and uniqueness theorems for ODEs and systems of ODEs
- Define Laplace transform
- Describe how numerical methods approximate the solution to an ODE or a system of ODEs
- Describe the qualitative solution of an ODE or system of ODEs including equilibrium solutions, sinks, sources, saddles,centers and separatrixes
- Determine the general solutions and specific solutions to a linear, constant coefficient system of ODEs
- Explain what is meant by a qualitative solution to an ODE
- Explain, both geometrically and analytically, the importance of eigenvalues and eigenvectors in determining thesolutions for a system of linear ODEs
- Justify basic theorems, including the Linearity Principle, about ordinary differential equations
- Model applied situations with ordinary differential equations (ODEs) and with systems of ODEs
- Outline the general process for solving ODEs using Laplace transforms
- Show that a proposed solution to an ODE or system of ODEs is or is not an actual solution
- Sketch the bifurcation diagram associated with a given family of autonomous ODEs
- Sketch vector fields, direction fields and slope fields associated with a given ODE or system of ODEs
- Solve ODEs using separation of variables, integrating factors and guess-and-check, as appropriate
- Transform higher order linear ODEs into systems of first order ODEs

**MTH261 Linear Algebra **

Credits 4Spring

**Registration Requirement:** MTH252 with a grade of "C" or better.

This course is a study of vectors, matrices, systems of equations, linear transformations, determinants and eigenvectors, primarily in the setting of finite real vector spaces (though examples of other spaces are used in context). Students are introduced to formal proof writing. This course provides the linear algebra necessary for the study of multivariable calculus, differential equations and abstract algebra. A CAS-capable calculator is required (e.g. TI-nSpire CX CAS or TI-89).

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Use vector notation and operations in applied and purely symbolic situations. [Objectives 1-11]
- Use matrix notation and operations in applied and purely symbolic situations. [Objectives 12-19]
- Describe and apply properties of vector spaces. [Objectives 20-28]
- Create and use linear transformations in applied situations. [Objectives 29-33]
- Define and calculate eigenvectors and eigenvalues. [Objectives 34-36]
- Apply linear algebra in a variety of situations. [Objectives 37-39]
- Write and interpret formal proofs. [Objectives 40-41]

**MTH275 A Bridge to Upper-Division Mathematics **

Credits 3Winter

**Registration Requirement:** MTH251 with a "C" or better; RD090 and WR090, or IECC201R.

This is a bridge course designed to help students transition from computation-based mathematics to the more proof-based curriculum typical of junior and senior collegiate-level mathematics courses. Students will construct and validate proofs, explore the nature of mathematics, and navigate some of the systems and conventions used within the mathematics community. Prerequisite MTH251.

### View Course Outcomes:

- Develop and negotiate mathematical conventions to communicate ideas;\\n\\n
- Develop conjectures about mathematical topics.\\n
- Develop definitions (and axioms as necessary) that are needed to prove conjectures.\\n
- Provide informal arguments to support or refute conjectures;\\n
- Refine informal arguments to produce mathematical proofs;

**STAT243Z Elementary Statistics I (Course offered online) **

Credits 4Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH105/MTH105Z or MTH111/MTH111Z; each with a grade of "C" or better.

A first course in statistics focusing on the interpretation and communication of statistical concepts. Introduces exploratory data analysis, descriptive statistics, sampling methods and distributions, point and interval estimates, hypothesis tests for means and proportions, and elements of probability and correlation. Technology will be used when appropriate.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Critically read, interpret, report, and communicate the results of a statistical study along with evaluating assumptions, potential for bias, scope, and limitations of statistical inference.\\n
- Produce and interpret summaries of numerical and categorical data as well as appropriate graphical and/or tabular representations.\\n
- Use the distribution of sample statistics to quantify uncertainty and apply the basic concepts of probability into statistical arguments.\\n
- Identify, conduct, and interpret appropriate parametric hypothesis tests.\\n
- Assess relationships in quantitative bivariate data.

**STAT244 Elementary Statistics II **

Credits 4Summer/Fall/Winter/Spring

**Registration Requirement:** RD090 and WR090, or IECC201R and IECC201W; and MTH243/STAT243Z; each with a grade of "C" or better; or placement above stated course levels.

This course gives a deeper look into inferential statistics; including formal construction of confidence intervals & hypothesis tests of one and two populations, Analysis of Variance, goodness-of-fit & contingency tables, linear regression & prediction intervals for bivariate data, data collection techniques & experimental design, probability theory using contingency tables normal distributions, and discrete & binomial probability distributions. Computer software experience is provided. A culminating project, in which students gather samples, make inferences regarding populations & present their findings is required. Use of actual data & interpretation of statistical results are emphasized.

**This course fulfills:** Non-Lab Science

### View Course Outcomes:

- Conduct formal hypothesis tests for means, proportions, difference of means and difference of proportions
- Construct and interpret formal confidence intervals for means, proportions, difference of means and difference of proportions
- Create and deliver a statistical report including graphical representations of data, analysis of possible sources of bias in sampling, an examination of statistical significance and a conclusion
- Create probability distributions for binomial random variables and use them to calculate probabilities
- Design and implement a statistical experiment to explore a causal association between two or more variables
- Evaluate simple, compound, and conditional probability statements using two-way tables
- Perform hypothesis tests for multiple parameters using the chi-square distribution (categorical parameters) or ANOVA (numerical parameters)
- Use formal theory to calculate Standard Error for the sample mean, sample proportion, difference of sample means, difference of sample proportions and sample correlation coefficient
- Use formulas to find the mean and standard deviation of binomial distributions
- Use technology to calculate probabilities and percentile values for normal and t-distributions
- Use technology to determine a least squares regression line. Determine a prediction interval for the response variable at any point along that line
- Use technology to perform linear regression for multiple variables

Course offered online

Cultural Literacy course