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Indeed, at most universities, a undergraduate-level course in discrete mathematics is a required part of pursuing a computer science degree.Many students’ complaint about traditional high school math—algebra, geometry, trigonometry, and the like—is The somewhat abstract nature of these subjects often turns off students.The mathematics of modern computer science is built almost entirely on discrete math, in particular combinatorics and graph theory.
While undoubtedly the subject matter being taught is important, the material (at least at the introductory level) does not lend itself to a great deal of creative mathematical thinking.
By contrast, with discrete mathematics, students will be thinking flexibly and creatively right out of the box.
In fact, one prominent MATHCOUNTS coach tells us that he spends nearly 50% of his preparation time with his students covering counting and probability topics, because of their importance in MATHCOUNTS contests.
Algebra is often taught as a series of formulas and algorithms for students to memorize (for example, the quadratic formula, solving systems of linear equations by substitution, etc.), and geometry is often taught as a series of exercises that are often done by rote (for example, the infamous ‘Two-Column Proof’).
We strongly recommend that, before students proceed beyond geometry, they invest some time Introduction to Number Theory textbooks, or by signing up for our introductory Counting and Number Theory classes—with very little algebra background.
Also see our article Don’t Fall into the Calculus Trap, which discusses the pitfalls of rushing into calculus too quickly and/or with inadequate preparation.As a child, perhaps you had a “problem of the week” to solve, perhaps on Fridays.Engaging with a word problem was your reward for getting through four days of worksheets and homework.On harder high school contests, such as the AIME, the quantity of discrete math is even larger.Students that do not have a discrete math background will be at a significant disadvantage in these contests.Rarely is this the case with most discrete math topics.When we ask students what their favorite topic is, most respond either “combinatorics” or “number theory.” (When we ask them what their least favorite topic is, the overwhelming response is “geometry.”) Simply put, most students find discrete math more fun than algebra or geometry.That binder might be organized by problem-solving strategies, like: working backwards; solve a simpler problem; or make a table or chart.Solving problems is not really something that can be taught like that.However, discrete math has become increasingly important in recent years, for a number of reasons: Discrete math—together with calculus and abstract algebra—is one of the core components of mathematics at the undergraduate level.Students who learn a significant quantity of discrete math before entering college will be at a significant advantage when taking undergraduate-level math courses.