Course Notes

CourseNotes: MAC 1105 College Algebra

I am your friend! - Calculator

I am your friend!

When I enrolled in college, my placement scores allowed me to skip college algebra. I decided to take it anyway because it had been several years, and I was sure I was rusty. I’m so glad that I took it. I’m currently studying calculus and analytical geometry, and I gotta tell you. If you’re taking algebra, don’t slack. If you do you will seriously regret it when you get to calculus. You can breeze through pre-calculus and trigonometry without being an algebra ninja, but not with calculus. It’s just like my calculus professor said–the hardest part about calculus is algebra. You’ll repeatedly use algebraic techniques that you thought you would never see again. The slope formula? That thing will beat you silly the first week in calculus if you don’t learn it now. In calculus, you will literally use everything you even just glanced at in algebra. Furthermore, your calculus professor will be disappointed that you didn’t see more things in algebra.

I don’t have a lot of advice for students taking algebra, but following are some of my thoughts. I’m sure your professor will drill it into you, but I should probably say it too… good note taking and practice are the key.

Modelling

Modelling problems, otherwise called “application problems” or “word problems” are often the most difficult part of mathematics for most students. It takes me more time to solve a modelling problem than it takes to solve other problems, in fact, I would even say that modelling problems are more difficult than other problems. However, where I differ from a lot of math students is the attitude I have toward them. I like them. I find them challenging. To me, they’re puzzles, and I love solving puzzles. There is a very real benefit to doing modelling problems and that is that it takes all that abstract mathematics and turns it into real, useful, tools.

Most of the modelling problems encountered in college algebra involve geometry, interest calculation, mixtures, uniform motion, rate of work done, or proportions. My suggestion is that you try to figure out a general procedure for each different type of problem. Some of these procedures involve the applications of formulas. For example, for simple interest calculations we use the formula I = prt (interest = principal * rate * time) and for uniform motion we use d = rt (distance = rate * time). For other types of modelling problems, you can learn specific tactics that make it easier to solve any problem of that type. For example, draw the problem if it involves geometry, and for mixtures; make a table. The takeaway here, is that general solutions/equations/procedures are extremely helpful when you’re ready to solve specific instances.

Absolute Value Equations and Inequalities

I’ve always had trouble with absolute value equations and inequalities, and so I think do a lot of other people. I try to remember the specific procedures, for example; |x| = a means x = a or x = -a, but come test time, I end up confused and unable to remember the procedures. The only thing that saves me is to think logically about a given case. It often helps me to draw a number line and then mark it up with interval notation and arrows to show the values that x can take.

When working with absolute value, it helps me to think of it as distance. For example |x – 3| is just the distance between x and 3. Distance is always positive–just like absolute value. If given the problem |x – 3| < 9, I would start by drawing a line with an arrow at each end (my number line). I know that the distance between x and 3 is less than 9, so I mark a spot for 3, a spot 9 units to the left of 3, and 9 units to the right of 3. I know that x must be between those outer two points in order for it to be within 9 units of 3. Then my answer is simply 3 – 9 < x < 3 + 9 or -6 < x < 12. What is |x|, you may ask? Well, it’s just the distance between x and zero.

Your Calculator

Your calculator is your best friend. Learn it well. Your calculator will save your life repeatedly when you’re in the midst of battling an exam… assuming you’ve learned how to use it. You must learn how to graph functions and use the trace and intersection features. This will allow you to double check your algebraic work as you go along. You also need to know how to enter an equation and then use the table and VAR features to try different values for x. These skills are guaranteed to save your ass and to save you time in the long run.

Also, be sure to read my post on avoiding mistakes in algebra.

Advertisements
Categories: College, Course Notes, Math | Tags: , , , | Leave a comment

Course Notes: ENC 1102 Written Communications II

enc-1102
I took ENC 1102 last semester, and finally, here are my thoughts on it.

ENC 1102 is the study of three forms of literature–short stories, poetry, and drama (plays). This course involves the critical analysis of various members of the aforementioned forms of literature. You have to really think about what you’re reading, break it down, analyze it, why this symbolism, why that allusion, and so on. I had to write one research paper during the course, and I chose William Faulkner’s “A Rose for Emily.”

One aspect of literary analysis that I’m not too fond of is the emphasis on interpretation. For any given classic, there seem to be hundreds of interpretations about the grander meaning or purpose of the work. One person says it’s about the idiocy of the North during the civil war, another says it’s about the silliness of the South during the civil war, another says it’s about the emergence of feminism, and so on and on and on. What if it was just meant to be an interesting story? Huh? Did you think about that possibility? What if the writer never harbored a hidden agenda that can only be teased out after months of speculation and tripping to conclusions?

As for reading drama, I don’t have too much to say about it–it’s just like watching the play in your head. After watching videos of the same plays, I realized that I enjoy the versions in my head better. During this course, I studied Hamlet for the first time, and after getting past the esoteric language, I actually enjoyed it and found moments that made me grin. The favorite play that I studied in this course would have to be Oscar Wilde’s The Importance of Being Earnest. Talk about LMAOing all over the floor…

What I’m about to say now may anger you and cause you to think condescendingly of me from hereon. This is particularly true if your major is literary in nature. Irregardless… just kidding. Regardless of how your opinion of my digital persona may change, the following things need to be said.

I’ll start in soft and easy…

To me, the purpose of writing is to convey information in an interesting manner. The best writers, then, are the ones that write unambiguously, and interestingly. It is quite the opposite with poetry. Petals on a wet, black bough? Bitch puhleeze! It takes a lot of effort for me to “understand” a poem, and even then, I can’t be sure that my interpretation is what the poet intended. I know that poetry is supposed to evoke emotion, but in me, the only evoked emotion is that of extreme irritation at the writer’s apparent inability to convey information in a clear and interesting manner. Poetry seems to be nothing more than a collection of vague verbal stimuli directed toward those that tend to find patterns in random nonsense. As such, it is more a verbal Rorschach Test than anything else. The fact is, ENC 1102 did nothing to mollify my unabashed hatred of poetry. I accept that I am missing out on a part of human experience that is important to many people, but that’s okay. I’ve come to terms with my condition.</end rant>

The only tip I really have, if you’re taking this course, is; if it’s a classic, and it tells a story; watch the movie.

P.S. Depending on your professor, you better wield your MLA with some serious skill (FYI: that last part included something called “alliteration.” You’ll learn all about that in ENC 1102).

Categories: College, Course Notes | Tags: , , , , , | Leave a comment

Course Notes: ENC 1101 Written Communications I

So much writing...

Write right!

Periodically, after completing a college course, I will publish some of my thoughts on the course. Hopefully, somehow, somewhere, they will help another undergraduate. This is one of those posts.

……………………….

To tell you the truth, when I registered for this course at my college, I didn’t expect to learn a lot from it. I considered myself a fairly good writer already, and no “beginner” writing course could possibly improve that. Could it? I registered for the course because it is a required undergraduate course for my school. Furthermore, it seemed like it would be an easy course–the perfect way to ease myself into college studies.

ENC 1101 focuses on grammar, MLA, and essay writing. The three required essays probably gives most college students the shivers, but with my enjoyment of writing, I approached them with little trepidation. It did turn out to be a pretty easy course for me; however, contrary to my initial thoughts, I learned quite a bit from it.

The most valuable thing I learned from this course is that commas are not to be sprinkled willy-nilly among the words. I had always approached comma usage at an intuitive level. To judge whether or not a comma was needed, I would simply insert it to see if it sounds right–clauses be damned. What I learned is that even something as seemingly nebulous as grammar, a subject with which I tended to rely solely on intuition, is governed by rules. To excel at grammar, those rules simply need to be learned.

By learning about the different types of clauses and the proper construction of compound and complex sentences, I now proof my essays in a much more systematic manner. Instead of simply reading it and trying to figure out if it sounds right, I now pick the clauses apart. Instead of making essay-writing more complicated, it’s actually made it easier. No more vacillating on whether or not a sentence needs a comma–just identify the clauses and apply the rules.

ENC 1101 was also my first exposure to the vast array of written resources available to college students. Prior to this, if I wanted to read a research paper, I was usually hit with a pay-wall. Now, I simply log in to my college’s library and access the paper through one of the hundreds of academic databases that my school is subscribed to. It’s amazing!

Learning how to properly document and cite (MLA) research sources is another important aspect of this course. I’ve learned that many professors are quite strict (read anal) about proper documentation. Not that it’s unimportant. It really is important. Plagiarism is despicable even if professors uses scare tactics to drill it into you.

TIPS

So, here are some tips that oozed out of the goo within my skull while I was taking ENC 1101:

Essay writing, particularly if you’re being scored by a college professor in a low-level writing course, is not art. This is not the time to be too experimental with your writing. It is commonly accepted by such professors that an essay requires three parts; introduction, body paragraphs, and conclusion. Furthermore, the introduction must contain an obvious thesis sentence, and all body paragraphs must have obvious topic sentences. Deviation from this structure is punishable by B’s and C’s. It gets worse. Sentences must be complete, and they may not be run on to each other. All of these rules may seem arbitrary but if you follow them, your professor will smile lovingly upon you. The good news is that all these rules can actually make it easier to write essays. Instead of blindly following your intuition, you now have checklists and precise recipes to follow. Personally, I feel that a carefully constructed essay reads contrived. My professor probably didn’t care what it made me feel like.

Improve your writing by writing a lot and striving to always use impeccable grammar.

How to analyze your own essay:

  1. Take a mental step back when you’re reading it. Pretend that someone else wrote it. How would you grade it? Why?
  2. Read it quickly. Does it flow? Is it alive? (If it’s alive, forward it to scientists. A living essay must surely be an unusual and wondrous species.)
  3. Read it slowly and analyze it–first by paragraph, then by sentence, and then by clause.

Sometimes when I write, I feel what I want to say, but the words just don’t flow from my head. In those cases, it often helps me to make it more personal. What words would I use if I was actually experiencing these things that I am trying to write about? Sometimes, it helps to change the setting. By picking the theme/subject out of the paragraph and throwing it into the midst of fighting spider-people on some alien planet, the right words might suddenly come to me.

Those, in an ordinary-sized nutshell, are my thoughts on ENC 1101.

Image credit: Pen image copyright (c) 2007 Fabio and made available under Attribution-NonCommercial 2.0 Generic (CC BY-NC 2.0)

Categories: Course Notes | Tags: , , , , , , , | Leave a comment

Create a free website or blog at WordPress.com.

Sean Carroll

in truth, only atoms and the void

The Intrepid Mathematician

Reading, writing and arithmetic.

The Life of an Ex-Amish Girl

My thoughts and feelings

What's new

Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao

Grownass Math

Bringing some fucking style to the math game.

elkemental Force

Research Notes on Energy, Software, and Life. By 'Subversive Elkement' Elke Stangl. Theory and Practice of Trying to Combine Just Anything.

a political idealist.

Lidia. 21. A college student with a blog dedicated to the thoughts and ramblings of the mind.

Many Worlds Theory

In one universe, this blog is about quantum mechanics. In another universe, it is not.

The Cheerful Chemist

Fascinating molecules and new developments in chemistry

Math with Bad Drawings

Math, teaching, copious metaphors, and drawings that will never ever earn a spot on the fridge

Post-Grad

Someone hire me. Please.

The Lazy College Student's Survival Guide

As a self-identified lazy college student with a High GPA. I will share my secrets to having an effective college education while not losing much sleep or life. Let's Go

mycollegelifeblog

Experience the joys of university life with me!

Why? Because Science.

Combating Stupidity Since 2012

My Digital Destiny

From carbon to silicon...