MATH 1201 — College Algebra

My personal experience and tips for this course

👋 Welcome to MATH 1201

Hi! If you are going to take MATH 1201 “College Algebra” at University of the People, this article is for you. I took this course from November to January of 2019–2020 and it was a very rewarding experience.

My most important advice would be to start this course without any preconceptions of algebra. If you start this course with an open mind and with the goal of succeeding and learning a lot during the process, you will be on your way to having a great experience.

If you are the kind of person that loves math and problem-solving (like me!), then you will find this course engaging and thorough. Throughout the course, the assignments ask you to apply the concepts that you are learning to real-world scenarios, which is awesome! ❤️ This is the aspect that I loved most about the course.

Be prepared to work hard from day one.

Do not underestimate the time that you will need to dedicate to this course. Solving the exercises and practicing requires time, in addition to the time required to complete your assignments, study, and assess your peers’ work. So be prepared and allocate the necessary time per week. Plan ahead.

💡 Tip: If English is your second language, then you will expand your vocabulary tremendously during this course.

📚 Course Content

Let me start by giving you a brief overview of the topics covered during the course. Even if you studied some of these topics during high school, I promise you that you will find many new and advanced aspects and concepts.

In particular, these are the topics covered per week (one unit per week):

• Unit 1: Functions
  During this unit, you will study relations and functions in detail. Particularly, you will learn the concepts of function, domain, range, piecewise functions, rate of change and local extrema. You will also learn the notation used to represent each one of these elements.

💡 Tips: During this unit, you will also be given the opportunity to review the prerequisites (Chapters 1 and 2) if you need to refresh concepts like real numbers, the order of operations, formula vs. equation, radicals, polynomials, inequalities, and absolute value. I really recommend reviewing these chapters even if you’ve studied them previously because you will find many details that you probably didn’t know.

• Unit 2: Graphs, Linear, and Quadratic Functions
  During this unit, you will study the graphs of basic functions and you will study linear and quadratic functions. Particularly, you will learn concepts like increasing function, decreasing function, constant function, slope and much more. In the chapter that covers quadratic functions, you will learn the general form of a quadratic function, its zeros, how to find its axis of symmetry, how to find its domain and range, and how to express a quadratic function in vertex form. This chapter is super interesting and applicable to real-world scenarios, so pay close attention to these topics.
• Unit 3: Polynomials
  During this unit you start learning about power functions and how they can be transformed and added to make a polynomial. You will learn many new things during this unit, including the Intermediate Value Theorem, division of polynomials, the Remainder Theorem, the Factor Theorem, the Complex Conjugate Theorem, the Fundamental Theorem of Algebra, the Linear Factorization Theorem, and Descarte’s Rule of Signs. You will also learn about rational functions and how to find their asymptotes.
• Unit 4: Composition and Inverses
  During this unit, you will learn how to combine functions and how to compose functions by taking the result of one function and using it as the argument for another function. This is very interesting, especially because the assignments ask you to find a real-world application of the topics covered during each unit, so you will learn how to use these principles in a real-world scenario. You will also learn how to find the inverse of a function and how to test if two functions are inverses and much more.
• Unit 5: Exponential and Logarithmic Functions
  During this unit, you will learn about these two types of functions which have a very close relationship, one is the inverse of the other. You will see how exponential models can be applied to model real scenarios and how these two types of functions are graphed according to their domain and range. You will also learn the properties of logarithms (the product rule, the quotient rule, the power rule) and the change-of-base formula. This unit presents very interesting models such as logistic growth.
• Unit 6: Systems of Equations
  During this unit, you will learn how to solve systems of linear and non-linear equations and inequalities. You will learn how to identify the different types of systems of equations: dependent, independent, and inconsistent. You will learn how to express the solution of a system of equations, even if the system is dependent and there are infinite solutions. You will also learn to solve systems of linear equations using Gaussian elimination to find the row-echelon form. This chapter was very interesting! 😃
• Unit 7: Foundations of Trigonometry
  During this unit, you will learn essential concepts of trigonometry such as angle, coterminal angles, complementary angles, unit circle, sine, cosine, tangent, and inverse trigonometric functions. You will learn how to graph these functions and you will need to know how to identify their graphs, domain, range, and transformations.

💡 Tips: You might feel that this unit and the next one are a little bit more intense in terms of the amount of content that you need to learn, so I recommend dedicating more time during this period.

• Unit 8: Additional Trigonometric Concepts
  During this unit, you will learn about sinusoidal functions, their period and amplitude, and their features such as the range, domain, and asymptotes. You will also learn how to work with polar coordinates. I found this topic particularly challenging, so my advice would be to practice more and solve more exercises during this week. You will learn how to find the product and quotient of two complex numbers. This was completely new to me, so I found this topic very interesting, especially symmetry tests and the graphs of cardioids, Archimedes spirals, and rose curves. They are awesome! 🎉

✍️ Study Tips and Helpful Resources

Tip #1:

Solve the recommended exercises. Each week, you will find approximately 20 or 25 recommended exercises. My advice is to SOLVE THEM ALL. Each exercise has its corresponding answer in the final pages of the book, so you can check your work. If you don’t get the right answer at first, go over through notes again and try to find the mistake. This process of going through your solution and finding the mistake is an important part of the learning process as well. You can also ask in the discussion forums if you can’t find the mistake.

Tip #2:

Take detailed notes. Practice is based on the theory, so pay close attention to the theory and take detailed notes. During my time at UoPeople, I’ve developed a note-taking strategy that works for me, using highlighters and pens of different colors. Take some time to reflect what strategy works for you and try different approaches.

Tip #3:

This tool will be extremely helpful for you during the course:

Graphing Calculator - GeoGebra

It’s a free online graphing calculator that you will use to solve the exercises and for your assignments because in most cases you will need to graph the functions that you are working with and analyze them. You can start experimenting with it before starting the course to learn how it works.

Tip #4:

Familiarize yourself with the use of formal mathematical notation. The main textbook used during the course explains theorems and concepts using formal mathematical notation (the explanations themselves are very pedagogical and clear, but certain formulas and theorems have to be expressed formally). For your assignments you will need to express your work and findings using formal mathematical notation.

This is an example:

This skill is vital to succeed during the course and in future courses that require math. In addition, learning how to express your thinking process using technical terms and formal terminology is very important.

Tip #5:

Enjoy the learning experience. I think this is vital for every course you take at UoPeople. Being self-driven and motivated is key to succeed as an online college student.

✨ Good Luck!

I really hope you liked my article. Follow my Medium Publication My UoPeople CS Journey to read about my experience during the degree 🎓.

I wish you much success during this course and during your UoPeople journey! Your claps 👏 are much appreciated.