Navigating Freshman Math Classes: A Comprehensive Overview

Choosing the right math classes as a freshman, whether in high school or college, can be a daunting task. This article aims to provide a comprehensive overview of math course options, placement considerations, and pathways for students with varying levels of experience and interests.

Math in High School: Building a Foundation

Figuring out which math classes to study can be one of the most challenging parts of planning your high school schedule. Most high schools require students to take three years of math in order to graduate and recommend taking four years. Forty-five states have agreed to follow Common Core standards for math, which aim to create a more standardized math curriculum across the country. The math class you take freshman year will be chosen based on your previous math classes and any placement tests you may have taken before starting high school.

Common Core Curriculum

According to the Common Core Curriculum standard for Math, schools are required to cover six areas in high school math courses. These requirements often also include completing an algebra class and a geometry class. General areas of math include:

Number and Quantity
Algebra
Functions
Modeling
Geometry
Statistics and Probability

Therefore, according to the Common Core standards, a typical order of core High School Math curriculum from freshman to senior year is:

Algebra 1
Geometry
Algebra 2/Trigonometry
Pre-Calculus
Calculus

Typical High School Math Course Progression

For high school math, there is not a specific course you should be taking as a freshman, sophomore etc. However, schools may have different math course offerings, a typical progression includes Algebra I, Geometry, Algebra II, Pre-Calculus, and Calculus. This order is definitely not set in stone. Some schools teach algebra 1 and 2 back-to-back then move on to geometry, some schools include trigonometry with geometry or pre-calculus instead of algebra 2, and some students take pre-algebra or a similar course if they need to strengthen their math skills before taking algebra 1.

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Algebra I: Many students begin high school with Algebra I if they haven't taken it in middle school. Algebra I lays the foundation for higher-level math courses by introducing variables, functions, and problem-solving techniques. In this course, you’ll study topics ranging from expressions, systems of equations, functions, real numbers, linear questions, polynomials, quadratic equations, and functions. Students can be placed into this class for their freshman year, or other advanced math classes like Geometry or Algebra 2, based on their results of a placement test at the end of 8th grade beginning of their 9th-grade year.
Geometry: This course usually comes after Algebra I and introduces points, lines, angles, shapes, and their properties. Geometry can be essential for future courses as it helps develop problem-solving, logical thinking, and spatial reasoning skills. In the geometry class, you will study the relationships in geometric figures in a plane and in space, as well as mathematical methods such as deductive proof. The content is built upon Algebra I. If you have a strong background in algebra already, geometry may be an option for you to consider your freshman year.
Algebra II: Building on Algebra I concepts, this course covers more advanced algebra topics like linear and quadratic equations, systems of equations, exponential and logarithmic functions, and more. Algebra 2 is a course sequence built upon the foundation of Algebra I. Topics you will study include rational number exponents, functions, quadratic functions, and complex numbers, solutions of linear and quadratic equations, inequalities, absolute value equations, polynomials, exponential, logarithmic, and rational functions. Algebra II is typically required for advancement to higher-level math courses. Algebra II would be another possibility for you if you are confident in the math skills you built in middle school.
Trigonometry: Many schools integrate the topics covered in Trigonometry into Pre-Calculus class. Trigonometry class is built upon the foundation of Algebra II, with the goal of preparing you for Precalculus. In this class, you will study algebra content and the algebraic and graphical study of the six elementary trigonometric functions. Applies algebra and geometry skills to circular and periodic functions.
Pre-Calculus: This course bridges the gap between algebra and calculus, covering topics like trigonometry, complex numbers, and analytic geometry. Precalculus will provide you with profound knowledge in trigonometric functions, polynomial and rational functions, and logarithmic and exponential functions. Taking pre-calculus will better prepare you for college-level math courses, especially if you're considering a STEM major. You're unlikely to take pre-calculus until your sophomore year at the earliest. Pre-calculus will prepare you for taking Calculus or AP Calculus.
Calculus: Many competitive colleges appreciate seeing calculus on a prospective student's transcript, especially for STEM-focused fields. During Calculus, students can expect to continue the material taught in Pre-Calculus and begin to study differentiation and integration of the elementary functions, with an emphasis on problem-solving. Calculus is offered at various levels: AP Calculus AB (equivalent to one semester of college-level calculus) and AP Calculus BC (equivalent to two semesters of college-level calculus). This is considered the advanced high school math courses you will take If your school offers these options, you may want to consider taking at least Calculus AB. You'd likely be taking calculus in your senior and/or junior years, depending on how quickly you progress through the previously listed courses.

Advanced Placement (AP) Courses

For students who’re interested in STEM majors in college, taking AP classes such as AP Statistics, AP Calculus AB, or AP Calculus BC is an important jumpstart in the college application.

AP Calculus AB: Explore the concepts, methods, and applications of differential and integral calculus. Generally equivalent to the 1st semester of college-level calculus.
AP Calculus BC: Explore the concepts, methods, and applications of differential and integral calculus. This class includes all the content covered in AP Calculus AB and adds additional topics including parametric equations, polar coordinates, and vector functions, as well as infinite sequences and series. Generally equivalent to the 2 semesters of college-level calculus, allowing students to start in multi-variable calculus in college.
AP Statistics: Explore major concepts and tools used for collecting, analyzing, and drawing conclusions from data. This AP course covers exploring data, sampling and experimentation, anticipating patterns, and statistical inference.

Honors Classes

Besides regular and AP classes, schools will also offer honors mathematics classes. Honors classes are taught with greater depth and breadth at a higher pace and are suitable for students who want and can handle challenging and advanced math topics.

Math Electives

If you want to take a specific math class or simply love math and want to take more math classes, there are several options for you. Statistics is one of the most common math electives, and it is useful for many career fields. You can take statistics at the AP level or regular level. Other math electives include computer math, math literacy, and math applications.

Computer Science: Computer Science courses are real-world applications of math, with classes ranging from Algorithms to Graph Theory with Python, depending on the school. The focus of computer science electives is to provide you with knowledge about real-world application of math as well as introductory knowledge about programming. The College Board offers two AP Computer Science exams:
- AP Computer Science A: Learn the concepts and tools of computer science through the Java programming language. Then, apply the knowledge learned to design, write, and test computer programs that solve problems or accomplish tasks.
- AP Computer Science Principles: Learn the principles that underlie the science of computing and develop the thinking skills that computer scientists use. Students work on their own and as part of a team to creatively address real-world issues using the tools and processes of computation. This class teaches more of the concepts of how computers work and is recommended for students without knowledge in the area.

Considerations for College Admissions

Like high schools, most colleges require applicants to have completed three years of math and recommend four years. For students planning on majoring in humanities, the social sciences, or a similar field, the math classes you took in high school will not be as important to colleges because they'll be looking more at the classes that relate to your intended major.

If you plan on majoring in a STEM field (science, technology, engineering, or math), expectations will be higher because math skills will be more critical to your college courses and future career. Most colleges will require you to have taken four years of math in high school, sometimes including pre-calculus and calculus. Regardless of what you plan to study in college, it is highly recommended that all high school students complete four years of math because many colleges expect it, even if they don't require it, and it will help you stay prepared for any math classes you may have to take in college.

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Math in College: Finding the Right Starting Point

Figuring out what class level to start in math can be challenging! You are not the only one and many students have had to do the same. Most students come into Harvard not knowing exactly what they want to study and that is wonderful and encouraged. Many students are interested in STEM and that means they will likely need to take a math course. Students come from many different backgrounds when it comes to math - from taking precalculus in high school to taking college level math courses in high school. Because of this, the math department offers a lot of different introductory courses in math to fit the needs of every student.

Placement Tests and Advising

Students take a math placement test in the summer before they matriculate onto campus as first years. This placement result provides a suggested course based on the student's proficiency on the exam. Please consult First Steps in Math for assistance in selecting an appropriate course.

Introductory Course Options at Harvard

Besides Math MA and MB, there are other introductory courses for students who have already taken calculus in high school. Math 1A also explores single-variable calculus, but in a more condensed way than Math MA. Math 1B explores integration, series, and differential equations. Math 18 and 19 cater to specific subjects with Math 18 teaching multivariable calculus for the social sciences and Math 19 teaching multivariable calculus for the life sciences. There is also a newer course called Math QA and QB which explores quantitative analysis for economics and the social sciences. For those students who took AP/IB or advanced math courses in high school and already learned single variable calculus, there is the Math 21 series, Math 21A and 21B. Both are offered in the fall and spring semesters. Math 21A covers multivariable calculus and Math 21B covers linear algebra and differential equations. For those students inclined to learn more about real analysis, students can take Math 22A and B that cover the same material, but add introductory real analysis to the course as well to give students a chance to learn about writing proofs. Math 25 covers theoretical linear algebra and real analysis, and Math 55 covers real and complex analysis as well and algebra and group theory. While all of these are considered introductory classes, they can be taken whenever it works for the student's schedule. For example, I took Math MA and MB, Math 1B and then Math 22A and Math 22B. The reason these are deemed introductory classes is because once you have the foundational skills learned in one or more of these classes, you can then take any other math class and also other STEM courses. It is important to note that no one takes all of these classes, you choose which ones to take based on your academic background and interests. You can learn even more about math at Harvard here.

Math MA: Math MA serves as an introduction to calculus and really takes a deep dive into derivatives and limits with the emphasis on self-discovery and a mastery of the understanding behind concepts and methods.
Math 1A: Also explores single-variable calculus, but in a more condensed way than Math MA.
Math 1B: Explores integration, series, and differential equations.
Math 18: Teaches multivariable calculus for the social sciences.
Math 19: Teaches multivariable calculus for the life sciences.
Math QA and QB: Explores quantitative analysis for economics and the social sciences.
Math 21A: Covers multivariable calculus.
Math 21B: Covers linear algebra and differential equations.
Math 22A and 22B: Cover the same material as Math 21A and 21B, but add introductory real analysis.
Math 25: Covers theoretical linear algebra and real analysis.
Math 55: Covers real and complex analysis as well and algebra and group theory.

Academic Support

MATH 1006 - Academic Support for MATH 1106, MATH 1011 - Academic Support for MATH 1110, MATH 1012 - Academic Support for MATH 1120, MATH 1021 - Academic Support for MATH 2210 are available that reviews material presented in lectures, provides problem-solving techniques and tips as well as prelim review. Provides further instruction for students who need reinforcement. Not a substitute for attending lectures or discussions.

Course Examples at Wright State

The Department of Mathematics and Statistics offers first-year mathematics and statistics courses that meet the general education and major requirements for all undergraduate disciplines at Wright State. All prerequisites must be met before registering for any math or statistics class. Developmental math (DEV) classes are offered through Foundation Studies.

MTH 1450: An application of mathematics to modeling real-world problems from the behavioral, computational, managerial, and social sciences. This course is for students in science programs who are not required to take the regular Calculus courses. Completion of this course does not automatically place students in a regular calculus course.
MTH 1140 & 1150: This is the first course of the 2-course sequence on math fundamentals required for students in elementary and middle childhood pre-service teachers programs in the College of Education and Human Resources. Overview of mathematical topics from a perspective appropriate for early and middle childhood educators. Number systems such as whole numbers, fractions, rationals, and decimals. Place value and bases. The meaning of and algorithms for the operations of addition, subtraction, multiplication, and division.
MTH 2070: Discrete mathematics useful in computing.
STT 2640: This is a survey course in the basic statistical concepts and methods, mostly required by programs in nursing and psychology. An introduction to the fundamental ideas of statistics. Numerical and graphical methods for finding and summarizing important features of data. Principles of designing experiments for collecting data. Introduction to probability. Use of statistical computing package to apply methods and illustrate concepts. Confidence intervals and hypothesis testing introduction. Applications to means, proportions, two-sample comparisons, contingency tables, linear regression, and analysis of variance.

Course Examples at Lehigh University

Each program has different requirements regarding what mathematics courses are needed. Students should consult the Course Catalog to determine the mathematics courses that are required and recommended by different degree programs.

MATH 005: Introduction to Mathematical Thought (3 credits): This course introduces students to the meaning, content, and methods of mathematical thought. The course considers mathematical topics of interest for their own sake, rather than for specific applications. Topics used for illustration will vary. Students do not need a strong high school mathematics background. Math 005 is well suited to students majoring in the humanities. The mathematics content is ‘real,’ and students should expect to perform mathematics.
MATH 012: Basic Statistics (4 credits): This course provides a foundation for the statistical description and analysis of data, which are fundamental issues in the social sciences. Students in certain social science programs take MATH 012 while students in natural sciences and engineering typically take a different statistics course such as MATH 231.
MATH 043: Survey of Linear Algebra (3 Credits): This course introduces students to linear algebra. This is the mathematics underlying Google search engine, Markov chains (which have applications in many areas of natural and social sciences), the analysis of big data, as well as many other areas of application. Students in engineering and some programs in sciences will take a different linear algebra course such as MATH 205.
MATH 000: Preparation for Calculus (2 credits): This course is for students who need more preparation before moving on to calculus. This 2 credit course does not count toward the total number of credits required for graduation or the math distribution requirement, but the grade does count in the student’s GPA. Students taking MATH 000 should pass with a grade of C- or better before taking MATH 051, 021, or 075."
MATH 50s SEQUENCE:
- MATH 051: Survey of Calculus I (4 credits)
- MATH 052: Survey of Calculus II (3 credits) The 50s sequence covers much of the material covered in the 20s sequence but not in as much depth, allowing the material to be completed with fewer credits (totaling 7 credits). This sequence is suited for Architecture, Biological Sciences, the Pre-Health Track, and some Natural Science and Economics programs. MATH 021 is usually an acceptable substitute for MATH 051 but not the reverse, and MATH 021 is an acceptable prerequisite for 052 but 051 is not a prerequisite for 022; students with strong mathematics backgrounds might consider starting with the 20s sequence if they have any question about which sequence best suits their curriculum.
MATH 081: Calculus with Business Applications (4 Credits): MATH 081 is a first semester calculus class aimed at students in business and economics. MATH 081 is usually an acceptable substitute for MATH 051 but not the reverse. Students in the College of Business and Economics meet their calculus requirement with MATH 081 or MATH 021 or the sequence MATH 075 and MATH 076. MATH 051 does not satisfy this requirement. MATH 081 is not an acceptable replacement for MATH 021. Students who want to take MATH 022 and further mathematics courses should take MATH 021.A follow-up course, MATH 082 Calculus with Business and Economics Applications II is also available to students who plan to study in areas of business and economics that are particularly quantitative. Students with interests in such areas should consult with the Department of Mathematics and with their advisors for more information.
MATH 20s SEQUENCE:
- MATH 021: Calculus I (4 credits)
- MATH 022: Calculus II (4 credits)
- MATH 023: Calculus III (4 credits)
- MATH 075: Calculus I part A (2 credits) - offered in fall only
- MATH 076: Calculus I part B (2 credits) - offered in spring only All or part of the 20s sequence (12 credits) is required of all engineering students as well as majors in Mathematics, Statistics, Computer Science, and many Natural Science and Economics programs. The three semesters cover single- and multiple-variable calculus and introduce differential equations. MATH 075 and 076 (2 credits each) divide the material of MATH 021 into two semesters for those who are not prepared to go directly into MATH 021.

Finding Your Community

As a Math MA student, I loved collaborating with my peers, going to the Math Question Center to work on problem sets and then going to Brain Break after (the nightly snack bar provided at the first-year dining hall and in the upperclassmen houses). Math MA was truly a community of math learners and is the perfect places for enthusiastic first years to meet other students and begin their math journey at Harvard.

Tips for Success in Freshman Math Classes

Take Placement Exams Seriously: These exams are designed to assess your current knowledge and recommend the most appropriate starting point.
Seek Academic Support: Utilize resources like tutoring centers, academic support programs, and professor office hours.
Build a Community: Collaborate with peers, form study groups, and participate in math-related activities.
Consider Your Interests and Goals: Choose courses that align with your academic interests and potential career paths.
Don't Be Afraid to Ask for Help: Math can be challenging, so don't hesitate to seek assistance from professors, teaching assistants, or classmates.

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