The world of abstraction is simultaneously magical and daunting. Mathematical puzzles can delight with surprise, but often at the cost of massive headaches. As a math student, I’ve borne the scars of banging my head against pure algebra but couldn’t resist the allure of a new area called Contemporary Mathematics.
Contemporary Mathematics is a freshman college course that targets students who are not learning a STEM discipline. The course aims to give these students thinking skills by surveying areas in pure and applied mathematics. The emphasis is on using a range of fundamental concepts to everyday problems.
To get a clearer idea of what’s involved, it is worth considering the motivation for offering the course and reviewing the typical modules of contemporary mathematics.
The Rationale For Contemporary Mathematics
The traditional offerings of college-level mathematics are Pure Mathematics, Applied Mathematics, and Statistics. Pure Mathematics covers the general theory of mathematics in an abstract way. Applied mathematics considers the technical application of mathematics to science. Statistics courses cover the analysis, interpretation, and presentation of data.
The problem with this curriculum is that it has limited practical use for non-STEM students:
- Pure mathematics has limited practical use and is prohibitively technical to many students.
- Applied mathematics and statistics serve only a narrow set of STEM-related careers.
Contemporary Mathematics has been designed to repurpose mathematics to fit recognizable situations for students who are not actively learning STEM fields. It is a course that provides students with habits of mind that help navigate the real world, not specialist technical careers or abstract theoretical concerns.
Contemporary Mathematics Curriculum
There is no single curriculum, as it may vary from college to college. We provide an overview of modules that are typically included in a Contemporary Mathematics course.
1. Critical Thought
Critical thinking replaces impulsive intuitive action with systematic reasoned thought. Key to the definition is the ability to frame relevant questions that pinpoint areas of activity needed to solve a problem and illuminate the path to solving them.
In this module, the mathematician’s approach to solving a problem is the focus rather than the specifics of the situation. This approach is taught without invoking distractive technicalities.
2. Set Theory
Set theory is the basis of abstract algebra. A set is a collection of objects, and any algebra involves a set of structural constraints imposed on a set. By engaging with the no-frills basic units of algebra, Contemporary Mathematics students get to practice the abstract reasoning of mathematicians without confusing structures.
This module involves basic set operations and everyday applications, allowing students to practice abstract mathematical modeling.
3. Number Theory
Being numerate is a life skill on a par with being literate. College-level mathematics assumes that the student has acquired this skill before college. In Contemporary Mathematics, there is explicit attention to working with number systems. This can be regarded as advanced school math.
The focus here is on understanding why there are different counting systems, being comfortable with which one to choose (e.g., discrete vs. continuous) in different contexts, and mastering basic operations.
This module overlaps somewhat with Set Theory, Computer Science, and even Analytic Philosophy. Logic complements Critical Thinking in that it presents rule-bound constraints on the formation of beliefs. Understanding and applying logic leads to well-ordered thoughts.
The approach in Contemporary Mathematics is to introduce the laws and structure of Propositional Calculus from an intuitive point of view, based on argument in natural language. Propositional Calculus is the most basic system of logic, corresponding to Set Theory.
5. Personal Financial Management
Financial Management draws basic concepts from the Mathematics of Finance to present a toolkit for solving everyday budgeting and financial planning problems. This is the area that speaks the loudest to the need to equip non-STEM students with technical acumen.
Students will learn to apply the correct method to a given financial problem. Applications include calculating interest on bank deposits, evaluating investment returns, and understanding basic currency and cryptocurrency calculations.
6. History Of Mathematics
By showing how mathematical ideas develop in relation to each other and in response to concrete problems, students get an improved understanding of the nature of mathematics. The multicultural history of mathematics is indicated, showing its ubiquitous on human development.
Successful students will understand Greek ideas about solids, the Arab invention of algebra as a counting system, and appreciate the accomplishments of Hindu and Chinese mathematicians.
Here students learn to think mathematically about space and physical objects. As regards content, there is much overlap between the treatment of geometry in High School and College-level Contemporary Mathematics.
The key difference is that in Contemporary Mathematics, the abstract theory is closely yolked to physical applications. E.g., Pythagoras’s much-taught theorem is applied to the measurement of circumferences, along with allied geometric concepts.
In Contemporary Mathematics, the interest in statistics is twofold. First, it teaches that there are mathematical methods for handling uncertainty. Second, it shows how to draw on these methods to characterize problems of uncertainty faced in real life and thereby handle risks.
A core subcomponent is expectations theory, which teaches how to quantify the likely outcome when a series of probabilistic scenarios is imminent. This skill lives adjacent to financial management, as some everyday financial problems (e.g., as regards insurance) are statistical in nature.
Contemporary Mathematics FAQ
Many questions often pop up when students are offered CM courses in college.
Do I Need To Learn Contemporary Mathematics?
Contemporary Mathematics is not a compulsory prerequisite to anything. If you are already learning a STEM-related discipline like Computer Science or Engineering, this course will not fulfill your course criteria and be redundant.
Non-STEM students should consider the benefits of learning a different and helpful thinking style.
Is Contemporary Mathematics New?
“Contemporary” is not a reference to the content of the course. It traverses ideas that have been around for hundreds of years. Math Literacy has been offered for decades as a survey course for outsiders. What makes Contemporary Mathematics current is that it surveys the present state of mathematical ideas.
Is Contemporary Mathematics Hard?
Contemporary Mathematics is easier to learn than Pure or Applied Mathematics. It leans on basic concepts and ideas from mathematical sciences. However, it is a fully-fledged college course and subject to the standards of the institution offering it. Don’t expect a walkover.
Is Contemporary Mathematics Part of STEM?
Contemporary Mathematics should be considered part of STEM education, in spite of its lack of vocational application.
Can I Major In Contemporary Mathematics?
Contemporary Mathematics is an introductory course offered only at the freshman level. Anyone looking to major in mathematics should do so only if they are comfortable with their High School mathematics performance, and preferably in consultation with a vocational advisor.
Which Jobs Is CM Good For?
There are no jobs that require Contemporary Mathematics. This course is taken only for its ability to gain insight and cultivate new behavior. Students with an interest in STEM-centric jobs are advised to consult an advisor.
What Is The Best College For CM?
This is largely a matter of taste. If you’re not committed to a college, shop online before deciding.
What Are The Prerequisites For CM?
These vary between colleges. Generally, some High School mathematics is required. Some institutions will substitute an entry exam in the absence of High School math.
How Can I Become A Contemporary Mathematics Teacher?
A qualified Mathematics teacher with a broad interest should be able to migrate to Contemporary Mathematics with ease. You will be dealing with students who are less comfortable teaching themselves mathematical concepts, so the emphasis is on your pedagogic, not technical skill.
How Can I Learn More About Contemporary Mathematics?
If you are a student, browse online for colleges prospectuses. These give a good idea of the areas covered and the learning outcomes expected. Details differ between institutions.
As an educator, the same online resources will guide you to employment opportunities. Specialist journals track developments in the field and offer guides for curriculum development.
Mathematicians and engineers shouldn’t have all the fun. By taking a Contemporary Mathematics course, liberal arts and other non-STEM students can enhance their cognitive toolkit by dipping into a range of concepts from the mathemagician’s box of tricks.