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Calculus

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Transcendental number. The difference between teaching and instruction. A brief discussion with a reader of my personal blog (profkeithdevlin) reminded me once again of the common confusion between instruction/training and teaching/learning.

The difference between teaching and instruction

As a child, I never experienced what I would now call mathematics teaching. (I revised my understanding of what teaching is, when, as an adult, I saw it in action on several occasions. Although I have no memory of having been taught that way, I guess it is possible that as a very young child I was.) What I was presented with at school was instruction. The quality varied a lot, but looking back it was definitely instruction, not teaching. I quickly figured out how to play that game successfully – success in that case being measured by my being able to solve under exam conditions, problems like the ones the teacher had shown us and we had practiced in class and done for homework.

The technique I mastered early for succeeding in that regime lasted me all the way through to calculus and on into university. Easy Access Study Guide. IntegralCALC Academy online courses. The Calculus Controversy. Understanding the Derivative. Math 124/125 - Calculus I Worksheets. APCalculusNMSI - Winplot. Section 4.2 Notes - Mean Value Theorem. Real Analysis: 6.5. Differentiable Functions. Why these ads ...

Real Analysis: 6.5. Differentiable Functions

Having discussed continuity we will turn to another class of functions: differentiable functions. This group of functions is one of the focus points of Calculus, and you should already be familiar with many aspects of those functions In our setting these functions will play a rather minor role and we will only briefly review the main topics of that theory.

As usual, proofs will be our focus point, rather than techniques of differentiation as it has been in Calculus. First, we will start with the definition of derivative. The usual geometric interpretation of the derivative at a point is as slope of the tangent line to the graph of f(x) at the point (c, f(c)). Implicit Functions. One way to get at the implicit functions embedded in a "mixed-up" equation is to graph all of the pairs (x, y) that balance the equation.

Implicit Functions

For example, we have noted that if then Here the equation implicitly defines two perfectly normal functions, and it is a simple matter to plot them together: Other cases are harder. For example, This is the famous Folium of Descartes. Www.math.dartmouth.edu/opencalc2/cole/lecture24.pdf. Algebraic Function Tricks of the Trade. Algebraic Function Tricks of the trade What to expect when graphing algebraic functions.

Algebraic Function Tricks of the Trade

TI-84 Plus Silver Emulator. Thousands of college students in Ontario need help with grade school math. Students complete basic math tests.

Thousands of college students in Ontario need help with grade school math

Reuters photoEnterprising tutors may want to pack up their calculators and head toward Ontario's post-secondary institutions. A recent study by York University and Seneca College in Toronto has found that thousands of Ontario's first-year community college students have signed up for basic math courses in order to brush up on skills they should have mastered in junior high. As Parent Central reports, the study's authors said their findings raise a red flag over the quality of math instruction in the province and could also indicate a growing lack of interest in math that may hurt the economy over time.

"We're expressing concern that 8,300 students are taking preparatory and foundational math in first-year college, but the vast majority cover concepts introduced in Grades 6, 7 and 8," co-author and York University professor emeritus of math Graham Orpwood told Parent Central. Podcasts - A Brief History of Mathematics. A screenshot that illustrates what peer instruction can do - Casting Out Nines. How to design video games that support good math learning: Level 5 « profkeithdevlin. Procedures or thinking?

How to design video games that support good math learning: Level 5 « profkeithdevlin

Part 5 of a series The vast majority of video games that claim to teach mathematics do not actually do that. Rather, what they do is provide a means for students to practice what they have already been taught. For the most part, the focus is on basic computational skills. A good example is the first-person shooter Timez Attack. Such games are the low hanging fruit for the math ed video game designer, and like most low hanging fruit, it has pretty well all been picked, leaving game designers coming into the math ed space having to look elsewhere for a useful application of their talents. The difficulty hits you as soon as you decide to go for more than mastery (ideally to fluency) of already taught basic computational skills.

This distinction is to a great extent relatively recent. For the Göttingen revolutionaries, mathematics was about “Thinking in concepts” (Denken in Begriffen). It’s your call which view of mathematics you take, pre-1850 or post. On Your Mark. Tips for mathematical handwriting. John Kerl kerl at math dot arizona dot eduFeb. 25, 2007 Now that you’re majoring in one of the technical disciplines (engineering, science, or math), you’re going to be spending a significant amount of time communicating in writing with others.

Tips for mathematical handwriting

You may find that previously unimportant details, such as crossing your z’s, now become essential — not only so that others can understand you, but also so that you can avoid mistaking your own 2z for z2 and so on. This is especially important if your handwriting (like mine!) Is less than perfect. Before I continue, take a fresh look at our Roman alphabet, the digits, and the Greek alphabet: Notice that these mechanically typeset symbols are all clear and distinct (except that lowercase omicron and most of the uppercase Greek letters look like Roman letters — we don’t use these “duplicates”). When we write by hand, though, symbols can become ambiguous — we’re not machines, and things get a little loopy when we hurry.

Lowercase Roman letters: Volume of Revolution - The Disk Method.