Why Math Is College Critical: Crunching Numbers After High School
Every year, millions of high school seniors breathe sighs of relief upon finishing their final exams before university, thinking they’ll never again have to find x, do derivatives, or convert degrees into radians on their TI-84s.
And, every year, millions of incoming freshmen schedule their first university math classes shortly after Googling, with exasperation and dread, “Do you have to take math in college?”
In this article, let’s explore not just why math is important to a well-rounded college education, but also the different types of math – and, therefore, its related challenges – that students encounter upon beginning their college careers.
A Rude Awakening: An Introduction to Math Classes in College
College-level math presents for many students a sharp learning curve. Application-based word problems, solvable upon simply identifying the correct formulas to use, give way to lectures about the theoretical and abstract. Those who were comfortable with high-school “mental math” must face unfamiliar leaps in logical and conceptual complexity. Even finding help with homework online may require more original searches and Internet sleuthing than ever before.
While some high schools try to give their students a strong “foundation” for university-level depth, most freshmen are still in for a rude awakening. Before giving any advice, let’s at least learn what to expect.
Reviewing Different Types of College Level Math
College students come from a wide array of educational backgrounds, so it’s important to establish a baseline understanding of what college level math problems might actually look like. In this section, we’ll elaborate upon the levels of math through which students progress all the way from high school to graduate study.
Keep in mind that not all of these levels form distinct, hermetically isolated fields. Part of what makes mathematics so fascinating, albeit sometimes frustrating, is that its different concepts are constantly communicating with each other, allowing mathematicians always to build upon and apply their prior knowledge to new situations.
Stairway to… Heaven? Climbing the Levels of Math
When you think about it, the interplay of mathematical fields makes perfect sense. In elementary school, students progress from learning basic arithmetic to pre-algebra to their first forays into variables and equations. There’s no reason why high school should not continue that progression, nor why the transition to college math should somehow disrupt it.
We say this not to pretend that college math is not a difficult adjustment – as we’ve established, it is – but to emphasize that its challenges are not insurmountable. By mastering these fundamentals, there’s no reason to panic nor think, with rigorous studying, that you cannot succeed.
Mastering Geometry: The One That “Shapes” Students’ Conceptual Skills
We’re starting with geometry because it often marks students’ first opportunity to understand mathematics not just in terms of numerical operations, but as a world of consistent proofs and principles.
One of the oldest mathematical fields, geometry forces students to conceptualize angles, dimensions, and other properties of objects. By dealing with real-world problems, geometry enables students to expand their understanding of math’s practical applications. However, by teaching exercises in logical thinking, it also empowers them to confront future math courses dealing heavily with theories and abstractions. Therefore, geometry constitutes an early bridge through which students begin to approach higher-level math.
Mastering Trigonometry: A True “Sine” of Maturity
While its five syllables sound intimidating, the rest shouldn’t be. As a subset of geometry, and often not even occupying its own course, trigonometry simply refers to the study of the properties of triangles. To succeed in trigonometry, students must learn relationships between angles, sides, and their corresponding ratios known as “sine,” “cosine,” and “tangent.”
Trigonometric applications are historic and highly variable, ranging from astronomy to navigation to finding the heights of buildings. While not the most complex subject here, mastering “trig” is still necessary for students who, when taking college math, would rather have bigger things to worry about.
Mastering Precalculus: An “Integral” Part of College Prep
For those who don’t take AP Calculus, “precalc” is often the last math class students take in high school. And for good reason; with its focus on introducing new principles, getting adequate precalculus help before graduating allows you to prepare for the transition to college-level math.
Combining geometry, trigonometry, and algebra, precalculus gives students a chance to practice concepts that are explored in full-on calculus. These include graphing inequalities, convergent and divergent series, and the first whispers of calculus terms like derivatives and integrals. While far-reaching in scope, precalculus is entrenched in skills that many students have spent years building.
Mastering College Level Algebra: Navigating the “X”-tra Work
Having taken Algebra 1 and Algebra 2 beforehand, most freshmen have some experience with formulas, equations, and using symbols to represent numbers. But how does college make such things more complex? At what level is college algebra, exactly?
College algebra still teaches functions, quadratics, and exponents, but in more depth, with more abstract reasoning, and at a faster pace. You’ll be expected to study, keep up, and understand new material after less practice than you’re used to. Therefore, while seemingly less necessary than other subjects, seeking college algebra homework help is never an unhelpful way to set up for success.
Mastering Statistics: “Polling” Your Own Weight
College marks the first time many students encounter statistics, or the study of drawing conclusions about large “populations” by analyzing data from representative “sample” groups.
In some ways, stats is less dependent upon “math” calculations than the concepts it requires students, likely for the first time, to learn, like correlation, tests of significance, and regression analysis. As a means of estimating population data, its inherent imperfections can frustrate those who take satisfaction in getting exact answers. That said, statistics is among the most practical, applicable forms of mathematics, and studying it in college is hardly regrettable in the long run.
Mastering Calculus: “Changing” With the Times
It’s often seen rightly as “the big one.”. Invented by Isaac Newton and Gottfried Leibniz, calculus is the study of change. Want to know how fast a pool drains when it’s raining? Or how to chart a planet’s orbit while accounting for the Sun’s gravitational pull? Or, even, how quickly medicine starts to act on the human body?
Calculus is complex, but it has vital importance in physics, engineering, economics, and other major fields. Students might need calculus homework help to understand ever-intensifying limits, derivatives, and integrals, but doing so will yield ever greater academic enrichment in the long run.
Academic Prerequisites: Math Courses Required in College
Let’s return to the question with which we started: Is math a requirement in college? At American universities, the answer is likely “yes.”
Even for humanities majors, math credits are necessary to fulfill general education curricula. At Arizona State University, for example, every student must pass general college mathematics, college algebra, precalculus, or any other more advanced course. Similarly, Rutgers University requires that all students, alongside subjects like English Composition, attain three credits in logical and quantitative reasoning.
Though these classes may sound like a headache, they don’t have to weigh down your GPA with the right attention and focus.
Getting Ahead of College Math: Some Useful Summer Programs
For those who want to prepare adequately, summer math programs for college students are an effective way to stay in front of any impending math prerequisites. For those who are committed to studying higher-level mathematics, such programs create opportunities to meet like-minded students and produce original, often collaborative contributions to mathematical research.
In either case, pursuing additional studies outside of the conventional school year shows dedication, persistence, and commendable work ethic. These three programs vary in attendance and exclusivity, but in doing so they demonstrate that students, should they only look for them, can find resources that suit their individual needs.
An Early Start: The Stanford University Mathematics Camp
Often the world of college preparation, perhaps spurred by watchful parents, begins well before students start to write the Common App. That’s why programs like Stanford University’s Mathematics Camp (SUMaC) cater to rising juniors and seniors who seek advanced mathematical enrichment, not to mention the chance to study at one of the world’s premier research institutes.
SUMaC runs every June and July, combining online with “residential” curricula. Given that students attend before college application season, the program constitutes a strong résumé booster while uniting future university trailblazers in their dedication to number theory, algebraic topology, and other relevant academic subjects.
“Think Deeply About Simple Things”: The Ross Mathematics Program
Located in both Columbus, Ohio and Terre Haute, Indiana, the Ross Program invites motivated pre-college students to spend six weeks attending intensive lectures and discussions on number theory. Since 1957, the program has trained future leaders in math, business, and scientific fields.
Apart from its academic advantages, Ross also gives recent high school graduates an early chance to experience college life. Students are organized in small “family groups,” live in dorms, and must be responsible for their own schedules. For soon-to-be freshmen worried about leaving home, the program thus offers a headstart on not just academic but social and emotional development.
The Pre-Ph.D. Track: The Bernoulli Center for Fundamental Studies
Headquartered in Lausanne, Switzerland, the Bernoulli Center invites a select group of prospective researchers from around the world to attend its Young Researchers in Mathematics summer program.
The central goal of YRM, which covers all expenses for participants, is to produce and publish a collaborative research project over the course of one week. Though selective, the program gives aspiring mathematicians the chance to engage in professional academic study, make international colleagues, and gain some experience abroad at a prestigious Swiss institution. Though applications are closed for this year, the Bernoulli Center keeps general program information updated and publicly available here.
Why Does This Matter, Anyway? The Overall Importance of Math
In times of budget cuts, the arts and humanities are often the first to face constriction. Therefore, it seems we’re more likely to hear impassioned defenses of why studying literature, history, or theater matters for social and cultural enrichment.
These defenses are quite correct, but their prominence implies that it’s obvious why the “other stuff,” like math, also matters.
For our purposes, math learning is important because it teaches critical thinking, creativity, and a similar set of personal attributes transferable to almost any analytical discipline. In this section, let’s explore the specific benefits of studying math and, for good measure, some practical learning tips.
The Soft Skills: Why Math Matters
More than almost any other subject, studying math equips students with essential “character” assets – qualitative over quantitative skills – that facilitate success in diverse fields. If that seems counterintuitive, just remember that college courses appreciate mathematics not just in terms of concrete operations, but also for its abstract and theoretical depth.
These “soft” skills include communication, independent problem-solving, logical reasoning, collaboration, and even reading comprehension. In the long run, employers value these qualities because they make employees dependable, adaptable, and easy to work with. For students, they prove that studying math is not just “job training,” but a means of achieving a well-rounded, enriching education.
The Hard Skills: The Practical Applications of Learning Math
Of course, learning math also teaches students specialized skills that unlock unique opportunities in STEM careers. These include training in statistical analysis; advanced calculus; linear algebra; and courses which directly prepare students for specific fields, like “applied engineering mathematics.”
While many math majors pursue jobs in accounting or actuarial sciences after graduation, the hard skills they learn along the way thus allow for welcome flexibility. Therefore, studying math is also important because it empowers “mathematicians” to become statisticians, computer programmers, financial analysts, data scientists, and much else. For all of its challenges, math is important in opening worlds of possibility.
Lastly, Some Practical Advice: How Best to Study Math
Finally, here are some tips for learning math at university:
- Don’t cram. Take initiative and study a little bit every day. Math is conceptual; concepts take time to absorb. Building knowledge incrementally will strengthen your foundation for the next exam and future ones.
- Read the textbook. Sometimes the wording is confusing, but they’re better than relying only upon disorganized lecture notes. Plus textbooks contain useful exercises that, with repetition, can hammer home new material.
- Do every practice set. Don’t do four problems and assume you “get it.” Practice for each scenario, and encounter the most difficult ones before your exam.
College Math and the Path to Success
We’ve discussed various aspects of studying math in college: whether it’s necessary (it is), what it actually looks like, and how you can prepare before and during university for its newfound challenges.
In the end, “how much” math you learn in college depends upon what you choose to study. But whether you’re meeting a prerequisite or a full-on mathematics major, it’s incumbent upon you to remain attentive, develop useful study habits, and utilize all resources that can help you succeed. Grades are important, but also is math more broadly – in terms of professional training, skill-building, and simply providing enrichment in each student’s academic life.