What in the hell is "pre-calculus"? Apparently, I get to teach it next year. There's a book. Sure, I could just say what is in the book, but... the book is crap.

It's got a Chapter 0. I always cringe when I see a Chapter 0. This tells the students about sets, complex numbers, quadratic functions, linear equations, matrices, probability, and statistics. I think sets are a bit of a hard-on for Bourbaki that won't much relate to their next two years of math. Statistics seems better handled *after* Calculus, but some probability and combinatorics seems good. Matrices seems like a distraction, too.

Chapter 1 is about functions. Fine, but it includes continuity, end behaviour, and limits. Won't that be in the first semester of Calculus?

Chapter 2 is about Power, Polynomial, and Rational Functions. Fine.

Chapter 3 is Exponential and Logarithmic Functions. Great.

Chapter 4 is Trigonometric Functions. If one thing fucks over Calculus student in universities, it's that trigonometric functions are only vaguely understood. Shouldn't I spend more time with this?

Chapter 5 is Trigonometric Identities and Equations. Fine. This needs practice, but in none of this is there ever an introduction to the unit circle.

Chapter 6 is Systems of Equations and Matrices. Is this necessary?

Chapter 7 is Conic Sections, which frankly, seems like a better point of departure than Chapter 1. I mean, these kids just had conic sections in Algebra 2.

Chapter 8 is Vectors... okay... I guess it's pre-calculus with the assumption they'll see Calculus-based Physics....

Chapter 9 is Polar Coordinates and Complex Numbers. I'd pair this with the Conic Sections? Also, I'm not sure if they'll revisit this in Calculus.

Chapter 10 is Sequences and Series. Ok, this they need.

Chapter 11 is Inferential Statistics, which seems more related to other fields they may be studying.

Chapter 12 is Limits and Derivatives. Is this like all the "post WW2" stuff in the history book that the publisher was pretty sure you'd never make it to? It also seems to repeat Chapter 1.

I never had a "pre-calc" class. This book is problem based and my own formation was proof-based. Does anyone have a book they favored? Is there a standard set of knowledge for "pre-calc"? Is it supposed to coordinate with their other classes? What would be in your dream class for "pre-calc"? I'd rather just have one semester of trig, including spherical trig, then a semester of analysis with an emphasis on trigonometric functions.

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[–] [deleted] 0 points 2 points 2 points (+2|-0) ago (edited ago)

[–] pitenius [S] 0 points 0 points 0 points (+0|-0) ago

Thank you for understanding my complaint. I could put together the Calculus course in less than an hour. Pre-Calc? gah...

[–] [deleted] 0 points 1 points 1 points (+1|-0) ago

[–] phw 0 points 1 points 1 points (+1|-0) ago

I got an intro to this at the end of precalc. It's hard to do it right unless a student is already ready for calculus.

Trig is great if they learned it in Euclidean geometry. At this level it's almost easier to spend a class on Euler's formula and say everything you need to know about trig identities is a special case of this one. (I guess you still need the geometric interpretation for word problems and such.)

Systems of equations is very necessary for calculus and elsewhere, but introducing matrices is unnecessary overhead for this task. Doing elimination on the equations directly may take a little more paper than row operations, but they're less likely to fuck it up. Combining these subjects into a single chapter risks confusion the next time they see a matrix in some other context. (How do I

solve a matrix?).Vectors after matrix equations? (sigh) They won't need this much in single-variable calculus and multi-variable calculus won't trust you to have taught it, but it wouldn't hurt to them at least understand enough to use parametric equations.

Agreed.

This, along with combo and prob, is all good stuff to have in the toolbox, but really deserves to be in its own course.

[–] pitenius [S] 0 points 0 points 0 points (+0|-0) ago

Would you stick with the book or strike out on your own?

[–] phw 0 points 0 points 0 points (+0|-0) ago (edited ago)

Most Precalc books I've seen are pure cashgrabs with little value beyond what can be had for free (eg Stitz&Zeager, or the discards of last year's version that are probably stacked in the hallway of your math department). If your students have already bought the book or if your department needs the kickbacks when they do, then just use the book. In any case, feel free to skip/reorder sections or add topics to do in more detail as makes sense to you.

[–] rwbj 0 points 1 points 1 points (+1|-0) ago

In my calc courses, it was implicitly assumed most of the students were already familiar with limits/continuity/etc. We were at the definition of derivatives using limits within a week or so. Not long after that we were onto l'hopital's rule and racing forward from there. And this was a 3 semester version of calculus! Jumping into derivatives without a solid understanding of limits (which you do not get in what was basically a 3 lecture 'refresher') is very possible, but it leaves your fundamental understanding completely hamstrung. I would make it a goal to see that the kids could jump straight into the limit definition of derivatives by the end of the course.

I think inferential statistics could be a handy applications topic. Imagine some sampling that seems to reach an asymptote based on some variable. For a really simple example maybe the percent of population that is a certain age. For less intuitive things, seeing this in terms of a limit could be informative. In any case, I think practical applications for what people are learning is extremely useful.

100% agreed on people having a piss poor understanding of trig in general. I absolutely love math, but somehow inexplicably never learned the most basic things about trig. For instance I only 'discovered' that cosine on a unit circle is is the x coordinate and sin is the y coordinate of a given degree until I got into game development years after university. That simple fact in turn meaning that sin can be derived from cosine or vice versa simply using the pythagorean theorem.

That's definitely an area that I think you could spend a lot of time covering - and there's countless interesting examples that can be shown. I like video game examples - a guy (starting at the origin) with a heading of 60 degrees walks forward 5 seconds with a speed of 1.2m/s - what are the coordinates of where he stops? Very simple stuff, but really really ingrains an intuitive understanding of trig. A way to test their understanding of the basic trig relationships would be to give them something similar to the above but instead of giving them a heading tell them that the cosine of his heading is √3/2 or something else that pythagoruses out nicely.

Seems like a fun course to teach specifically because of the lack of clarity. Gives you an opportunity to try to prep them as well as you see fit for calculus.

[–] pitenius [S] 0 points 0 points 0 points (+0|-0) ago

Yes and no. It's a small class, which will be nice, but there are some other limitations. It could be fun. I'm worried, but mostly because I'm trying desperately to figure out what information to impart and how to do it. In part, I have to actually open the class and see how the students learn.

[–] Grospoliner 0 points 1 points 1 points (+1|-0) ago

Pre-calculus is primarily an algebra course that focuses on functions, their properties, and behaviors. The course is intended to act as an introductory to calculus (hence the name) and a refresher for all previous math. It will build up a basis for college level calculus courses as they will not take the time to discuss things like exp, log, and trig functions basic behaviors outside the setting of calculus.

Sets are basis for linear algebra.

Continuity, limits, boundary conditions, etc, are typically covered in Calculus 1 (as they relate to calculus), along with differentiation and integration of functions (polynomial, trig, logarithmic, etc.; basically any function covered in Pre-calc).

Calculus 2 covers sequences, series, conics, and if I recall correctly, some applications of conics such as irregular bodies (surface area, centroids, centers of mass).

Calculus 3 typically covers multiple differentiation, integration, partials, and differential equations (so as to act as an intro to Diff EQ or 300 level math)

Systems of equations and matrices are both extremely important aspects for higher level applied math, like in physics and vector mechanics. An example is the modeling of the behavior of dynamic systems (such as an oscillating mass-spring system), wherein we use matrices along with differential equations to describe the system behavior. It is done in such a way so that it is simple to process and output results for things like buildings which have numerous components all reacting to some input.

The "conics" in pre-calc are things like parabolic and hyperbolic functions, analytic geometry. Analytic geometry forms the basis of kinematic behavior (objects in motion). These are simplified compared to their calculus or applied counter parts, but it is more exposure to subject matter not normally covered.

If they enter an engineering field, they will primarily handle all system input and output behavior as vectors. Vector mechanics is the basics of all physics.

Polar coordinate systems are covered heavily in calculus and are of particular importance in physics and engineering.

Not so much unless they're going to primarily study math. Series are used in some fields of engineering, but by the time someone gets to the point they're studying that, we've already developed lots of short hand methodology to by pass needing to work a series by hand (because engineers are lazy). It's good to know the foundation though, just so you have an idea of what is going on, also they're the basis of Calc 2.

More or less.

If you make it to this point, this is the end of semester preview material for the next level of class, Calc 1. So yeah. It's not mission critical to reach this, but like Chapter 10, it'll be nice to have an introduction. You won't get to Chapter 10 though. There's already too much material to cover just going up into Chapter 9.

Precalculus 6th Edition (Sullivan M.). Sadly I don't have a digital copy of it. However I do have digital copies of two other books.

Precalc 8th Ed(Larson)

Algebra & Trig 9th Ed(Sullivan)

Pretty much the topics these two text cover are standard fair for Pre-calc.

It's mostly an intermediary class between Algebra 2 and Calc 1. There's not really room for side by side course work for it.

Whatever course doesn't do "writing across the curriculum". That shit is terrible.

That seems like an application of multiple integration to me.

An entire semester devoted to trig functions? Seems like an awful long time to spend on just that. The entirety of Pre-calc is geared towards a 16-18 week period.

[–] pitenius [S] 0 points 0 points 0 points (+0|-0) ago

Fair enough, but I'm warning you: this is a year long course. Think about that when you estimate whether we'll crack chapter 10. (Keep reading to see how it stands now..)

Sets are "basic" for anything -- but they're not particularly useful. Indispensable for Abstract, but that's down the road a bit. We had radically different Calc 2 and 3. I'm not disputing the utility of any of the topics, but what I know is that this class feeds into Calc. A lot of these topics seem pretty extraneous for that class (which I've taught before). They'll need series for that, and in my experience none of them understand them at all. The prof who just abandoned this class told me he "didn't have time to get to them". Not knowing it makes Riemann sums difficult.

Thanks for the links. These books look a bit better. As another commenter noted, the selection of the text is not up to me. He was spot on. I have the options of following the book or working from scratch. I'm tending toward the latter, but I'm trying to rough out what they need for the Calc 1 class and what I can assume they have. I'm assuming anyone with any chance of Engineering or Physics will not be in this class, but they do have to have Calc 1 for several fields of study. That's what I meant by "coordinating with other classes".

I'd place the start of Spherical Trig with Menelaus (which reads surprisingly modern). No integration at all.

[–] Grospoliner 0 points 0 points 0 points (+0|-0) ago

Are you teaching at a high school or college level?

[–] SquarebobSpongebutt 0 points 0 points 0 points (+0|-0) ago

You act as if pre-calc is new or something. Been around for at least 27 years because I know people who took it in 1990.

[–] pitenius [S] 0 points 1 points 1 points (+1|-0) ago

Right. So... what's the "Fundamental Theorem of Precalculus"? I'll just start with that...

[–] SquarebobSpongebutt 0 points 0 points 0 points (+0|-0) ago

I assume prealgebra is also on your shit list. Look, some folks need to be spoon fed their shit and the education system has been willing to do so for a long time. Probably way before you were even born precalculus existed.

[–] pizza_mine 3 points -2 points 1 points (+1|-3) ago

My son just took his math placement test for UC Riverside. He was extremely worried and spent a lot of time reviewing calculus. He knew he wasn't ready. I calmed him down, it's not a pass or fail test it's just a measure. It's a measure of the math knowledge you understand. The university wants to start you off in the class that will best advance your math knowledge. He came out of the 3 hour exam and said, bah, it was easy it was all pre-calculus.

So my answer to you my teacher is fuck off. You want to make math easy? Teach it. Your entire list are things I learned by 10th grade high school. I was behind when I entered college.

My best answer to you is that you are a retard. Math is hard for people like you.

[–] Nietzsche__ 1 points 1 points 2 points (+2|-1) ago

You call him a retard and don't even realize he's a teacher and not the student. Sober up dipshit.

[–] pizza_mine 1 points -1 points 0 points (+0|-1) ago

Ok