# 0: Pre-Calculus Refresher - Mathematics

0: Pre-Calculus Refresher - Mathematics

The TSIA2, or Texas Success Initiative Assessment 2.0, is the updated version of the original TSI Assessment. This test consists of placement assessments for students who plan to attend a Texas public university or college. The exams are administered in Mathematics and English Language Arts and Reading (ELAR), and institutions use the results to help determine whether a student is ready for study at the college level.

The most notable difference is that the TSI test consisted of three exams (Reading, Writing, and Math), and the new TSIA2 uses only two (ELAR and Math). In the new version of the test, Reading and Writing assessments have been combined into one ELAR assessment. The TSIA2 exams are also scored differently, with a new range of college readiness benchmark levels.

## Math Insight

The usual trouble that people have with &lsquocalculus&rsquo (not counting general math phobias) is with algebra, not to mention arithmetic and other more elementary things.

Calculus itself just involves two new processes, differentiation and integration, and applications of these new things to solution of problems that would have been impossible otherwise.

Some things which were very important when calculators and computers didn’t exist are not so important now. Some things are just as important. Some things are more important. Some things are important but with a different emphasis.

At the same time, the essential ideas of much of calculus can be very well illustrated without using calculators at all! (Some not, too).

Likewise, many essential ideas of calculus can be very well illustrated without getting embroiled in awful algebra or arithmetic, not to mention trigonometry.

At the same time, study of calculus makes clear how important it is to be able to do the necessary algebra and arithmetic, whether by calculator or by hand.

## 0: Pre-Calculus Refresher - Mathematics

Algebra Review for PreCalculus

Algebra:
Mathematics branch of mathematics that uses basic operations to solve expressions

Linear equations:
A linear equation is an equation involving only the sum or product of constants and the first power of a variable.
y=f(x)=mx+b where m is the slope and b is the y intercept is the general form of an equation in slope intercept form.
The formula of a slope= where and are two points in ordered pair form.
The general form of point slope form is:
where m is the slope, and is the two points in ordered pair form.

Polynomial equations:
where a, b and c are constants of a quadratic equation is of the form
.

Factoring:
Factoring is a process of dividing out a factor from a mathematical expression.
Common factors technique is of the form ax+bx=x(a+b).
Difference of squares: .
Difference of cubes: .
Rationalizing is the process of removing an irrational expression from the numerator of a fraction.

Number line: An axis or ray usually horizontal on which real numbers are represented and ordered from left to right.

Absolute value: For a real number a, it is a if a is greater than or equal to zero or –a if a is less than zero. It is denoted.

Conic sections:
The general equation of a circle:
. Where r is the radius of the circle and is the center of the circle.
The general equation of an ellipse:
.

Natural logarithm: A log taken to base “e”, is approximately 2.7.

A review of the basic principles of algebra is needed to build a solid foundation for the usage of these skills in precalculus. Algebraic equations such as linear equations and quadratic equations are discussed in this particular tutorial.

A review of the basic rules of algebra is introduced here along with the basic definition of a linear equation and its graphical representation. Specific properties of linear equations are shown here with the use of examples. Polynomial equations with the use of examples are presented in this tutorial along with the factoring techniques used to factor them.

Specific Tutorial Features:

• Step by step easy explanation of example problems: slope, slope intercept, point slope form, quadratic formula, factoring polynomials, rationalizing, absolute value inequalities, circles, ellipses.
• Concept map showing inter-connections of concepts introduced.
• Definition slides introduce terms as they are needed.
• Examples given throughout to illustrate how the concepts apply.
• A concise summary is given at the conclusion of the tutorial.

See all 24 lessons in Pre-Calculus, including concept tutorials, problem drills and cheat sheets:
Teach Yourself Pre-Calculus Visually in 24 Hours

## Why Use Our Online Precalculus Calculator?

As mentioned above, mastering precalculus is essential if you want to meet great success during your math-learning journey. While hiring a tutor may seem like the best idea to achieve such a goal, doing so may prove to be difficult, or even impossible, for some people, be it because of budget restrictions, availability, or any other reason.

If you’re in that situation, a great alternative to which you can resort is using a precalculus calculator solver, an online one to be precise.

Mathway’s calculator for precalculus can be a great addon to your math-learning arsenal if:

If you’ve ever studied math, and you surely did since you’re reading this, you must know the struggle of graphing. Breaking down a problem is one thing, graphing is another. If you’ve had an issue with this aspect of precalculus, today’s your lucky day as our calculator for precalculus can prepare the graph for any function or problem you throw at it.

You simply have to open our precalculus graphing calculator, enter the problem, click on Show, and watch as the app solves everything in a matter of seconds.

Whether you’re a student or a parent trying to help their kid with math homework, you can’t avoid factoring when working on a precalculus assessment.

You can find factoring in problems involving exponents, simplification, and other topics, which makes mastering it a necessity.

Thankfully, not only is our tool the best graphing calculator for precalculus, but it also nails factoring among other operations.

As with all the other tasks, make sure to solve your problem yourself before resorting to our online calculator for precalculus, as that’s the best way to discover your mistakes and weak points and therefore improve and move forward.

Whether you lost your calculator, broke it, or simply forgot where you placed it, sometimes you have to find a way to solve problems related to precalculus without a calculator. Thankfully, that’s not a problem thanks to our phone app precalculus calculator. Why? Because it’s compatible with any device and you only need a moderate wifi signal or a valid data plan to use it.

Trying to solve precalculus combinations and permutations on a standard scientific calculator can prove to be quite the complicated task, especially if you’re not good with those devices.

If you need to perform certain probability tasks such as permutations and combinations without having to use your scientific calculator, you can open the precalculus calculator with steps free as it can show you how to solve such problems with ease through a step by step process.

## SEMESTER 1

Unit 1: Algebraic Functions

• Linear Equations and Their Graphs
• Functions Operations
• Inverse Functions
• Polynomial Division and Complex Roots
• Graphs of Polynomial Functions
• Graphing Rational Expressions
• Sketching Graphs Using Function Transformations

Unit 2: Exponential and Logarithmic Functions

• Exponential Functions and Their Graphs
• Logarithmic Functions and Their Graphs
• Properties of Logarithms
• Change of Base
• Rewriting Logarithmic Expressions
• Solving Exponential Equations
• Solving Logarithmic Equations
• Exponential Growth and Decay Models
• Logarithmic Models

Unit 3: Systems of Equations

• The Substitution Method
• Nonlinear Systems of Equations
• Solving Systems of Equations Graphically
• The Elimination Method
• Modeling and Optimization with Two-Variable Linear Systems
• Modeling with Non-Linear Systems

Unit 4: Topics of Analytic Geometry

• Introduction to Conics: Parabolas
• Finding the Standard Equation of a Parabola
• Applications of Parabolas
• Finding the Standard Equation of an Ellipse
• Graphing an Ellipse
• Applications of Ellipses
• Finding the Standard Equation of a Hyperbola
• Using Asymptotes to Sketch a Hyperbola
• Using Asymptotes to Find the Standard Equation

## Free Precalculus Diagnostic Tests

Precalculus courses are designed to introduce students to concepts integral to understanding Calculus, giving them a solid foundation on which to base the more complex ideas introduced in Calculus classes. Due to the quick pace at which many Calculus courses are forced to move, many do not spend much time on teaching or reviewing basic concepts this makes the class much more difficult for students who have not encountered basic Calculus concepts in Precalculus classes. Precalculus is thus highly recommended and often an enforced prerequisite for taking Calculus classes. By ensuring that you have a good grasp of the foundational concepts of Calculus introduced in Precalculus, you can set yourself up for succeeding in later Calculus courses and other advanced math classes. Whether you need top Pre-Calculus tutors in Albany, Pre-Calculus tutors in Milwaukee, or top Pre-Calculus tutors in Albuquerque, working with a pro may take your studies to the next level.

Precalculus builds upon concepts of functions and graphs that should be familiar to students from Algebra I and Algebra II courses. Precalculus covers the solving and graphing of functions, paying particular attention to the properties of functions, including domain, range, maxima, and minima, in order to teach students how to discuss and describe different aspects and properties of functions, which will come in very handy in Calculus courses. Precalculus also examines exponential and logarithmic functions, as well as the use of polynomials in functions and the effects exponents, logarithms, and polynomials each have on a function&rsquos graph. The way in which trigonometric and linear functions are each graphed is covered, and conic sections are explored, including those of ellipses and circles. Varsity Tutors offers resources like free Pre-Calculus Diagnostic Tests to help with your self-paced study, or you may want to consider a Pre-Calculus tutor.

Precalculus also covers sequences and series. In particular, the course examines both arithmetic and geometric series, and teaches students to solve problems dealing with the sums of infinite series, and the terms in a series.

Precalculus also introduces students to limits, an important quality of certain functions that is a foundational concept in Calculus. Students learn to solve for limits, including limits as x approaches infinity and one-sided limits. In addition to the Pre-Calculus Practice Tests and Pre-Calculus tutoring, you may also want to consider taking some of our Pre-Calculus Flashcards.

Fully understanding these important Precalculus concepts can drastically reduce the difficulty that you encounter in Calculus courses. Want to review or study some of these Precalculus and Calculus concepts right now? Varsity Tutors&rsquo free Precalculus Practice Tests are a source of multiple-choice Precalculus problems that you can use to review, study, or learn what you need to, when you need to. Each Precalculus problem comes with a complete, step-by-step answer, so if you miss one, you can figure out how to find the correct answer for the next time you encounter a similar problem. Problems are organized into Practice Tests, which draw from a wide variety of Precalculus topics, as well as by concept. So, if you only need to review problems that have to do with limits, you can select just those without having to bypass other problems that you will not find as useful, saving yourself time and allowing you to study in a targeted, efficient manner. By using Varsity Tutors&rsquo free Precalculus resources effectively, you can keep up with your Precalculus, review Precalculus concepts while taking more advanced classes, or get an idea of the topics and questions that await you in a Precalculus course you have yet to take. Good luck learning these important mathematical concepts!

## DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf An identification of the copyright claimed to have been infringed A description of the nature and exact location of the content that you claim to infringe your copyright, in sufficient detail to permit Varsity Tutors to find and positively identify that content for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to Your name, address, telephone number and email address and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

## Teaching Textbooks: Math 3 through Pre-Calculus When I first looked at Teaching Textbooks, I knew right away that this series was going to be popular among homeschoolers. These fantastic courses were designed specifically for homeschoolers in order to solve some of the issues that make math challenging for them. The courses are great for independent study since they are easy for students to use on their own, they require no work on the part of parents, and they are relatively inexpensive for sophisticated, computerized courses.

The Teaching Textbooks series is a college-prep curriculum even though it is not as rigorous as some other courses. Teaching Textbooks courses for the elementary grades move at a slower pace than most others. A student who excels and completes assignments quickly can always move through courses at a faster rate than others, but students are limited by the speed at which the app presents new material and problems. You might select a course at the level higher than the student’s actual grade. (That is why I label the series as appropriate for second through twelfth graders in the instant key.) Placement tests on the publisher’s website will help you select the correct level. Teaching Textbooks should be a particularly good choice for the student who has struggled with other math programs and needs a less pressured pace and style of delivery.

Students should aim to complete approximately one lesson per day, and the courses each have about 120 lessons. That should leave you many days in the school year for extra work on troublesome concepts, “mathless” school days, or getting a headstart on the next level.

The Teaching Textbooks courses have evolved over the years since they were first created, in keeping with technological advances. The latest version of each course, version 4.0, is sold as an app rather than as a physical product. Version 4.0 courses have a new feature that allows students to download up to six lessons at a time which can then be completed offline. This will make the courses usable even when good internet connections are lacking. The completed lessons sync up with the gradebook when students get back online.

The 4.0 apps can be loaded onto desktops, laptops, tablets, and phones, but a tablet will work best. The courses have a new scratchpad feature so that students can work out problems on their device, but this was designed for working on a tablet, and it won't work on a desktop. A desktop or laptop computer can still be used, but students will need to work out problems with paper and a pencil then enter answers into the program. Phones are probably not a very good choice since their smaller screens can be harder to read, and it might be more difficult to enter answers. Whatever device students use, they need headphones or a speaker to hear the lessons.

Only one student can use a course, and they have access for one year. Courses cannot be used by another student even if it is within the year. The cost for 4.0 courses has dropped from that of previous versions because there are no physical products, and large-family discounts are available. All of the courses have a free trial that includes the first 15 lessons. There is no time limit on using the free trial, and you can try out multiple courses. If a student has started working in a trial course, if you purchase that course, the student's data will be transferred into the complete course.

### How It Works

Parents create a student account, then students can log in with their own password. The apps present lessons directly to the student with audio instruction, animated lessons, and frequent interaction. Parents do not need to do anything but keep tabs on student progress.

Explanations are clear and complete, with plenty of practical examples and word problems. Students are frequently asked to identify items, enter answers, solve puzzles, or otherwise respond to the lesson material during the instructional component of the lessons. They are given immediate feedback and opportunities to correct their responses. For incorrect answers on problems, students can view the readily available solutions. Students take a quiz approximately every seventh lesson, and the frequent quizzes continually review previously learned concepts.

All answers are entered into the program, and it automatically maintains a running course average. So you can always tell how well students are doing. Daily emails are sent to parents to let them know what students have accomplished that day.

A lighthearted touch gives the courses a user-friendly feeling. This is evident in everything from the program's dashboard and the layout of the lesson screens to the cartoon animations and even the wording of the lessons. The basic screen designs are colorful, and students can add an animated buddy and a wallpaper background to personalize the display screen for the program. Students should have no problem figuring out what to do since the program is simple to navigate.

Prior versions of the courses had printed textbooks available, even though they weren't essential for those using computer-based versions of the courses. Version 4.0 courses have the complete textbook for that level built into the program as a searchable ebook. The ebooks include all of the instructional material and problems that are in the program, and you can print pages if you wish. (An answer key is also available within the program.) The ebook might be very useful for at least two reasons. First, parents can quickly scan the ebook to see what their child is learning or to get an idea of which topics are covered when. Secondly, printed pages can provide students with opportunities to practice doing math with paper and pencil and to work out the solutions for longer problems on paper. (Answers still need to be entered into the program to track student scores.)

The program's built-in grade-book feature shows parents detailed information. You can see scores on lessons as well as information on how students handled individual problems, including whether or not the student viewed a hint or solution or tried to answer a second time. Parents can manage student accounts from any device.

### Individual Course Details

#### Math 3

Math 3 covers addition, subtraction, multiplication, division, fractions, money, time, geometry, and measurement, plus a final lesson that introduces percentages. Much of the addition and subtraction instruction reviews concepts that should have been learned at earlier levels since it begins with simple addition and very gradually builds toward carrying and borrowing (regrouping). Instruction on other topics also reteaches the basics before moving on to more advanced concepts. Multiplication covers up through single-digit multipliers, and division teaches through single-digit divisors. Fractions are taught up through adding and subtracting fractions with common denominators. Numerous word problems help students with mathematical thinking and practical applications.

#### Math 4

Math 4 reviews concepts taught in Math 3 such as addition, subtraction, place value, carrying, and borrowing. It teaches new concepts such as rounding and estimating, multiplication, division, geometry, money, fractions, and Roman numerals. Reflecting the slower pace of Teaching Textbooks, concepts that generally appear earlier in other courses don’t show up till near the end of Math 4. Some examples would be multiplication by two-digit multipliers, long division, division with a remainder, and changing improper fractions to mixed numbers.

#### Math 5

Math 5 again reviews the basics, with the early lessons heavily focused on addition, subtraction, and multiplication. Both fractions and decimals are covered extensively at this level.

#### Math 6

Math 6 reviews the four basic arithmetic operations, place value, and time. It spends a great deal of time reviewing and teaching new concepts with fractions, decimals, and percents. It also covers geometry (points, lines, line segments, angles, area and perimeter for polygons, circumference for circles, and an introduction to geometric solids), units of measure (including the metric system), graphing concepts (e.g., thermometers, bar graphs, circle graphs), the order of operations, decimal remainders, equations, and probability. A remedial student with weak math skills might be able to pick up what he or she is missing since this course is fairly comprehensive on arithmetic basics. It might be too repetitive for a student who already has developed strong skills in basic operations. I mentioned earlier that the Teaching Textbooks series moves more slowly than many other programs, and it becomes more noticeable at this level.

#### Math 7

Topics taught in Math 6 are briefly reviewed. Then each topic is tackled at a distinctly more challenging level. For example, fraction instruction moves on to ratios. Percents include work with fractions and decimals plus real-life applications like commissions and sales tax. And geometry gets into computing the volume of solids. Also taught this year are statistics, probability, graphing, equations, inequalities, exponents, square roots, the Pythagorean theorem, and negative numbers.

#### Pre-Algebra

Pre-Algebra begins by revisiting whole-number operations, fractions, decimals, percents, and measurements. The rest of the course covers beginning algebra, negative numbers, exponents, roots, plane and solid geometry, functions, relations, graphing, statistics, probability, formulas (e.g., rate x time = distance), solving equations using the distributive property, and absolute value.

#### Algebra 1

Algebra 1 has more review of basic operations and pre-algebra concepts at the beginning than do some other first-year algebra courses, but it also has lessons covering functions, relations, statistics, probability, graphing with a calculator, the quadratic formula, absolute value, two-variable inequalities, and other more-challenging topics. Overall, topic coverage is similar to that of many other first-year algebra courses, but the explanations are more thorough. However, it is not as advanced as either Saxon's Algebra 1 or Shormann Interactive Math's Algebra 1.

#### Algebra 2

Algebra 2 covers topics such as second- and third-degree equations, systems of equations, roots, exponents, irrational numbers, logarithms, matrices, determinants, statistics, and probability. The course also includes practical applications in areas such as banking and physics plus word problems that help students understand how they might use algebra in the real world.

#### Geometry

Geometry uses a traditional Euclidean approach, beginning with a chapter on logic and reasoning, then moving on to definitions, postulates, and theorems. Formal proofs are introduced very early. Analytical geometry using the coordinate plane is reserved for the end of the course. As with the algebra courses, practical applications and occasional word problems help students understand how they might make use of geometry.

#### Pre-Calculus

The Pre-Calculus course includes problems modeled after those on the pre-calculus CLEP ® exam which should help students prepare for that exam. This is a challenging course that begins with functions and moves on from there. It covers various types of functions, such as polynomial, radical, and trigonometric. It also teaches triangle trigonometry, trigonometric identities, vectors and polar coordinates, systems, matrices, determinants, advanced analytic geometry, sequences, probability, and statistics. Special topics taught in the course include Pascal’s Triangle, The Binomial Theorem, Synthetic Division, More Sines and Cosines, Complex Numbers, De Moivre’s Theorem, and Fitting a Graph to Data.

### Pricing Information

When prices appear, please keep in mind that they are subject to change. Click on links where available to verify price accuracy.

Math 3 - Math 5: $43.08 per student per course Math 6 - Math 7:$55.08 per student per course
Pre-Algebra through Pre-Calculus - $67.08 per student per course subscription for 4-8 students -$199.08

You might want to check out the premade lesson plans from Homeschool Planet that are available for Teaching Textbooks. Find lesson plans available for this product at Homeschool Planet. Sign up for a 30-day FREE trial.

## Mathematics (MATH)

Prerequisites: None
Terms Offered: Summer, Fall, Winter, Spring
A study of functions and their algebra and graphs. Special functions of engineering and science are emphasized, including polynomial, trigonometric, and exponential functions and their inverses. Concepts and methods of algebra, trigonometry, and analytic geometry important to calculus are also emphasized. NOTE: While there are no pre-reqs for this course, enrollment is a result of Math Placement exam score. Failure to take this exam results in placement in MATH-100. Credits for MATH-100 do not apply to degree requirements. Also, placement in MATH-100 may delay entry in courses for which calculus is a prerequisite.
Lecture: 4, Lab 0, Other 1

MATH-101 Calculus I 4 Credits

Prerequisites: None
Terms Offered: Summer, Fall, Winter, Spring
An introduction to the theory and techniques of differentiation of polynomial, trigonometric, exponential, logarithmic, hyperbolic, and inverse functions of one variable. Also included are limits, continuity, derivative applications and interpretations. Computer software will be used to aid in understanding these topics. NOTE: Students can place into 101 with a sufficient score on the Math Placement Exam, or permission of Department Head.
Lecture: 4, Lab 0, Other 0

MATH-101X Calculus I 4 Credits

Prerequisites: None
Terms Offered: Summer, Fall
This course is for students showing a lack of proficiency in algebra and trigonometry on the Math Placement examination. The course contains the same material as MATH-101 but in addition, includes a review of algebraic expressions, trigonometic functions and their inverses, and analytic geometry. Computer software will be used to aid in understanding these topics. NOTE: Students can place into 101X with a sufficient score on the Math Placement Exam, or permission of Department Head.
Lecture: 4, Lab 0, Other 1

MATH-102 Calculus II 4 Credits

Prerequisites: MATH-101
Terms Offered: Summer, Fall, Winter, Spring
NOTE: Students also must receive a minimum grade of C in MATH-101. Riemann integration and the Fundamental Theorem of Calculus, including applications to area, volume, etc., and basic methods for conversion of integrals including change of variable, substitutions, partial fractions, integration by parts, improper integrals and numerical integration. Also introduced are sequences and series in one variable with emphasis on Taylor Series. Computer software will be used to aid in understanding these topics.
Lecture: 4, Lab 0, Other 0

MATH-102H Calculus II - Honors 4 Credits

Prerequisites: MATH-101
Terms Offered: Summer, Fall, Winter, Spring
Honors Calculus II is a deeper, more conceptual, rigorous, and limit based version of Calculus II (MATH-102). It is designed for students with strong mathematical skills. Riemann integration and the Fundamental Theorem of Calculus, including applications to area, volume, etc., and basic methods for conversion of integrals including change of variable, substitutions, partial fractions, integration by parts, improper integrals and numerical integration. Also introduced are sequences and series in one variable with emphasis on Taylor Series. Computer software will be used to aid in understanding these topics.
Lecture: 4, Lab 0, Other 0

MATH-102X Calculus II 4 Credits

Prerequisites: MATH-101 or MATH-101X
Terms Offered: Summer, Fall, Winter, Spring
This course is for students who want to improve their skills in Trigonometry and Differential Calculus. It contains the same material as MATH-102 but is taught at a slower pace and with more examples and sample problems. In addition, it includes reviews of Trigonometry and Differential Calculus.
Lecture: 4, Lab 0, Other 1

MATH-191 Mathematics Special Topics 4 Credits

Prerequisites: None
Terms Offered: As needed
This course is often offered as Pre-Calculus for Business, and in this form, available only to those students majoring in Business Administration. Course is equivalent to MATH-100.
Lecture: 4, Lab 0, Other 0

MATH-203 Multivariate Calculus 4 Credits

Prerequisites: MATH-102 or MATH-102H or MATH-102X
Terms Offered: Summer, Fall, Winter, Spring
A study of polar coordinates, parametric equations, and the calculus of functions of several variables with an introduction to vector calculus. Topics include surface sketching, partial derivatives, gradients, differentials, multiple integrals, cylindrical and spherical coordinates and applications. Computer software will be used to aid in understanding these concepts.
Lecture: 4, Lab 0, Other 0

MATH-203H Multivariate Calculus - Honors 4 Credits

Prerequisites: MATH-102H or MATH-102 or MATH-102X
Terms Offered: Summer, Fall, Winter, Spring
Honors Multivariate Calculus is an extended, deeper, more conceptual, rigorous, and limit-based version of Multivariate Calculus (MATH-203). The course is designed for students with strong mathematical skills. The topics include parametric equations, polar, Cartesian, cylindrical, and spherical coordinates, vector algebra, equations of lines, planes, and quadratic surfaces, calculus of functional of several variables, unconstrained and constrained optimization problems, multidimensional integrals, change of variables, and elements of vector calculus. Computer software will be used to aid in understanding these topics and for graphical visualization.
Lecture: 4, Lab 0, Other 0

MATH-203X Multivariate Calculus 4 Credits

Prerequisites: MATH-102 or MATH-102H or MATH-102X
A study of polar coordinates, parametric equations, and the calculus of functions of several variables with an introduction to vector calculus. Topics include surface sketching, partial derivatives, gradients, differentials, multiple integrals, cylindrical and spherical coordinates and applications. Computer software will be used to aid in understanding these concepts.
Lecture: 5, Lab 0, Other 0

MATH-204 Differential Equations & Laplace Transforms 4 Credits

Prerequisites: MATH-203 or MATH-203H or MATH-203X
Minimum Class Standing: Freshman
Terms Offered: Summer, Fall, Winter, Spring
An introduction to the principles and methods for solving first order, first degree differential equations, and higher order linear differential equations. Includes a study of the Laplace transform and its application to the solution of differential equations. Existence and uniqueness theorems for O.D.E.’s are also discussed.
Lecture: 4, Lab 0, Other 0

MATH-204H Differential Equations and Laplace Transforms - Honors 4 Credits

Prerequisites: MATH-203 or MATH-203H
Terms Offered: Summer, Fall, Winter, Spring
Honors Differential Equations and Laplace Transform is an extended, deeper, more conceptual, rigorous version of MATH-204. The course is designed for students with strong mathematical skills. The additional topics include Cauchy-Euler Equation, the Dirac Delta Function, Linear Models: Boundary Value Problems, Systems of Linear Differential Equations, and optional advanced topics, e.g. Power Series Solution and Solutions About Singular Points.
Lecture: 4, Lab 0, Other 0

MATH-258 Probability and Statistics 4 Credits

Prerequisites: MATH-102 or MATH-102X or MATH-102H
Minimum Class Standing: Sophomore 1
Terms Offered: Summer, Fall, Winter, Spring
This course introduces fundamentals of probability together with examples of discrete and continuous random variables, including Bernoulli, binomial, Poisson, normal, exponential and gamma random variables. Descriptive and inferential parametric statistics for one and two populations is covered. Correlation, simple and multiple linear regression, and single factor ANOVA are studied. A statistical package MINITAB or R is used throughout the course.
Lecture: 4, Lab 0, Other 0

MATH-291 Mathematics Special Topics 4 Credits

Prerequisites: None
Terms Offered: As needed
Mathematics Special Topics
Lecture: 4, Lab 0, Other 0

MATH-305 Numerical Methods and Matrices 4 Credits

Prerequisites: MATH-204 or MATH-204H
Minimum Class Standing: Sophomore
Terms Offered: Summer, Fall, Winter, Spring
An introduction to numerical methods including the study of iterative solutions of equations, interpolation, curve fitting, numerical differentiation and integration, and the solution of ordinary differential equations. An introduction to matrices and determinants application to the solution of linear systems.
Lecture: 4, Lab 0, Other 0

MATH-307 Matrix Algebra 4 Credits

Corequisites: MATH-102
Prerequisites: MATH-101 or MATH-101X
Terms Offered: Summer, Fall, Winter, Spring
A study of matrix concepts including such topics as basic algebraic operations, determinants, inversion, solution of systems of linear equations, vector spaces, basis and dimension, eigenvalues, and eigenvectors.
Lecture: 4, Lab 0, Other 0

MATH-308 Abstract Algebra 4 Credits

Prerequisites: (MATH-307) or (CS-211 and MATH-101) or (CS-211 and MATH-101X)
Minimum Class Standing: Sophomore
Terms Offered: Summer, Fall
Students will learn topics in modern algebra and will practice proof techniques. Topics will include: congruence classes, modular arithmetic, groups, subgroups, normal subgroups, Lagrange’s theorem, rings, subrings, ideals, quotient rings, isomorphisms and homomorphisms, polynomial arithmetic, fields, divisors, factorization, and proofs of the main theorems. The course is required for mathematics majors and is also useful in cryptography and quantum physics.
Lecture: 4, Lab 0, Other 0

MATH-313 Boundary Value Problems 4 Credits

Prerequisites: MATH-204 or MATH-204H
Minimum Class Standing: Sophomore 2
Terms Offered: Summer, Fall
An introduction to linear partial differential equations (PDE’s) and basic techniques of applied mathematics used to solve initial, boundary value problems associated with these equations. Topics include: derivation of some of the fundamental PDE’s’ and boundary conditions that arise in science and engineering Fourier Series Sturm-Liouville Systems including eigenvalues, eigenfunctions and eigenfunction expansions the separation of variables techniques Fourier Transforms. Applications to problems of science and engineering will be given throughout the course.
Lecture: 4, Lab 0, Other 0

MATH-321 Real Analysis I 4 Credits

Prerequisites: MATH-203 or MATH-203H or MATH-203X
Minimum Class Standing: Junior
Terms Offered: Winter, Spring of even years
A more advanced study of functions in one real variable including limits, uniform continuity, differentiation, integration, and sequences and series of functions topology of R.
Lecture: 4, Lab 0, Other 0

MATH-327 Probability & Stochastic Modeling 4 Credits

Prerequisites: MATH-203 or MATH-203H or MATH-203X
Minimum Class Standing: Sophomore
Terms Offered: Winter, Spring
This is a calculus-based introduction to probability theory and stochastic modeling. Students will learn fundamentals of probability, discrete and continuous random variables, expectation, independence, Bayes' rule, important distributions and probability models, joint distributions, conditional distributions, distributions of functions of random variables, moment generating functions, the Central Limit Theorem, laws of large number. Programming language R will be introduced and used throughout the course.
Lecture: 4, Lab 0, Other 0

MATH-328 Methods of Applied Mathematics 4 Credits

Prerequisites: MATH-204 or MATH-204H
Minimum Class Standing: Junior
Terms Offered: Winter, Spring of odd years
Topics from advanced calculus, dimensional analysis and scaling, perturbation and asymptotic methods, calculus of variations and integral equations. Applications of these tools to problems in engineering will be included.
Lecture: 4, Lab 0, Other 0

MATH-330 Biostatistics 4 Credits

Prerequisites: MATH-258 or MATH-408
Minimum Class Standing: Sophomore II
Terms Offered: Winter, Spring
This course covers topics in the design of experiments and data analysis useful in biostatistics including screening tests, analysis of categorical data, nonparametric methods, ANOVA and ANCOVA, nested designs, multiple regression, logistic regression and its extensions, design and analysis techniques for epidemiologic studies. Computer packages such as MINITAB or R will be used for all applications and the analysis of data sets.
Lecture: 4, Lab 0, Other 0

MATH-350 Financial Mathematics 4 Credits

Prerequisites: (MATH-102 or MATH-102X or MATH-102H)
Minimum Class Standing: Junior
Terms Offered: Winter, Spring of even years
This course provides an understanding of the fundamental concepts of financial mathematics, and how they are applied in calculating present and accumulated values for various streams of cash flows. These concepts are later used in reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. Key terms studied include inflation, rates of interest, term structure of interest rates, yield rate, equation of value, accumulation function, discount function, annuity, perpetuity, interest rate swaps and bonds. Procedures like determining equivalent measures of interest, discounting, accumulating,, amortization will be covered. Modern topics of financial analysis will be introduced, such as yield curves, spot rates, forward rates, duration, convexity and immunization.
Lecture: 4, Lab 0, Other 0

MATH-360 Life Contingencies I 4 Credits

Prerequisites: MATH-350
Minimum Class Standing: Junior
Terms Offered: Summer, Fall of even years
This course is an introduction to life insurance mathematics based on a stochastic approach. This course is to develop a student’s knowledge of the theoretical basis of certain actuarial models and the application of those models to insurance and other financial risks. Definitions of key terms will be studied, including actuarial present value, survival model, life insurance, annuities, and benefit premiums.
Lecture: 4, Lab 0, Other 0

MATH-361 Life Contingencies II 4 Credits

Prerequisites: MATH-360
Minimum Class Standing: Junior 2
Terms Offered: Winter, Spring of odd years
This is a continuation of Life Contingencies I. Development is based on a stochastic approach to life insurance models. Definitions of key terms will be studied, including benefit reserves, and multi-life and multiple-decrement models.
Lecture: 4, Lab 0, Other 0

MATH-412 Complex Variables 4 Credits

Prerequisites: MATH-203 or MATH-203H or MATH-203X
Minimum Class Standing: Sophomore
Terms Offered: Summer, Fall of even years
An introduction to the theory of complex variables. Includes basic algebra of complex numbers, analytic functions and the Cauchy-Riemann equations, elementary transformations, complex integration, the Cauchy integral formulas, Taylor and Laurent series, and the theory of residues.
Lecture: 4, Lab 0, Other 0

MATH-416 Vector Analysis 4 Credits

Prerequisites: MATH-203 or MATH-203H or MATH-203X
Minimum Class Standing: Sophomore 2
Terms Offered: Summer, Fall of odd years
An introduction to vector algebra and calculus including vector products, vector functions, and their differentiation and integration, gradients, line and surface integrals, conservative fields and potentials functions, Green’s theorem, parametric equations, curvature, and curvilinear coordinates.
Lecture: 4, Lab 0, Other 0

MATH-418 Intermediate Differential Equations 4 Credits

Prerequisites: (MATH-204 or MATH-204H) and MATH-305
Minimum Class Standing: Junior
Terms Offered: Summer, Fall, Winter, Spring
Systems of linear and nonlinear ordinary differential equations (ODE’s) will be studied.Topic include: systems of linear ODE’s, matrix methods, variation of parameters, and perturbation methods and boundary layers, phase portraits and stability of nonlinear ODE’s. Numerical methods for solving systems of ODE’s will be presented and used to solve physical problems of applied mathematics and engineering.
Lecture: 4, Lab 0, Other 0

MATH-421 Real Analysis II 4 Credits

Prerequisites: MATH-321
Minimum Class Standing: Junior 2
Terms Offered: As needed
An introduction to the study of real functions including metric spaces, normed linear spaces, Hilbert Spaces, and linear operators.
Lecture: 4, Lab 0, Other 0

MATH-423 Partial Differential Equations 4 Credits

Prerequisites: MATH-305 and MATH-313
Minimum Class Standing: Junior
Terms Offered: Winter, Spring of even years
This course is a continuation of MATH-313. Topics include Bessel’s equation and Legendre’s equation, boundary value problems in curvilinear coordinate systems, Green’s functions for ordinary and partial differential equations. Applications to problems of science and engineering will be given throughout the course.
Lecture: 4, Lab 0, Other 0

MATH-427 Statistical Inference & Modeling 4 Credits

Prerequisites: MATH-327
Minimum Class Standing: Sophomore I
Terms Offered: Summer, Fall of even years
A study of statistics including point and interval estimation, consistency and sufficiency, Minimum Variance Unbiased Estimators, Uniformly Most Powerful tests, likelihood ratio tests, goodness of fit tests, an introduction to non-parametric methods. Linear models, including regression analysis and Analysis of Variance are included. Programming in R will be introduced and used throughout the course.
Lecture: 4, Lab 0, Other 0

MATH-428 Sampling Theory 4 Credits

Prerequisites: MATH-327
Minimum Class Standing: Senior
Terms Offered: Summer, Fall of odd years
A study of sampling theory including probability sampling, simple random sampling, sample size estimates, stratified sampling, and cluster sampling.
Lecture: 4, Lab 0, Other 0

MATH-450 Statistics for Risk Modeling 4 Credits

Prerequisites: MATH-427
Minimum Class Standing: Junior I
Terms Offered: Summer, Fall
This course will prepare students to understand key concepts in the following categories of applied statistics: statistical learning, R programming language, construction of generalized linear models, regression-based time series models, principal components analysis, decision tree models and cluster analysis. Students will choose appropriate models, interpret model results and perform necessary calculations for statistical inference and prediction to answer the underlying business questions. Students are also assumed to have knowledge of probability and mathematical statistics.
Lecture: 4, Lab 0, Other 0