Math 20 Foundations Unit 1 Review: Fill & Download for Free

Freshman FallComputer Science 50: Introduction to Computer Science IGovernment 20: Foundations of Comparative PoliticsMath 21a: Multivariable CalculusSpanish 40: Advanced Language Review Through Literature and Culture IIFreshman SpringComputer Science 51: Introduction to Computer Science II: Abstraction and DesignExpository Writing 20: After the ApocalypseFreshman Seminar 33g: Eloquence Personified: How to Speak like CiceroMath 21b: Linear Algebra and Differential EquationsSophomore FallComputer Science 61: Systems Programming and Machine OrganizationEthical Reasoning 18: Classical Chinese Ethical and Political TheoryGovernment 1362: Democratic Citizenship and Public OpinionScience of the Physical Universe 26: Primitive NavigationSophomore SpringComputer Science 124: Data Structures and AlgorithmsComputer Science 171: VisualizationStatistics 104: Quantitative Methods for EconomicsUnited States in the World 31: American Society and Public PolicyJunior FallComputer Science 121: Introduction to Theory of ComputationComputer Science 182: Intelligent Machines: Reasoning, Actions, and PlanningGovernment 1072: Moral Issues in Contemporary PoliticsMusic 2: Foundations of Tonal Music IJunior SpringComputer Science 42: Controlling CyberspaceComputer Science 91r: Supervised Reading and Research (used for research in computer science pedagogy with David J. Malan)Science of Living Systems 20: Psychological ScienceCulture and Belief 48: God, Justice, and the Book of JobSenior FallApplied Computation 263: Data and Computation on the InternetComputer Science 175: Computer GraphicsComputer Science 205: Computing Foundations for Computational ScienceGovernment 1740: International LawSenior SpringComputer Science 207: Systems Development for Computational ScienceComputer Science 229r: The Mathematics of Data PrivacyComputer Science 277: Geometric Modeling in Computer GraphicsComputer Science 299r: Special Topics in Computer Science (used for research in GPU computing using OpenCL with Cris Cecka)Wish I Took (and will take online ASAP)Computer Science 161: Operating SystemsComputer Science 165: Data SystemsStatistics 110: Introduction to ProbabilityEconomics 10: Principles of EconomicsExpository Writing 40: Public Speaking PracticumGovernment 1540: The American PresidencyEthical Reasoning 22: Justice (though I audited)TaughtComputer Science 50: Introduction to Computer Science IComputer Science 164: Mobile Software EngineeringComputer Science E-1: Understanding Computers and the InternetComputer Science E-75: Building Dynamic WebsitesComputer Science E-76: Building Mobile Applications

Short answer: I don't know why you aren't good at math. I need more details about you to tailor an answer specifically to you about your specific needs, trials, & tribulations. I previously answered this in a fashion:Nick Campbell's answer to How did Alon Amit get so good at mathematics?But I'll try to answer it in a different manner here.Long answer:Since I can't answer this question specific to you and your individual issues, I'll try to answer in a generic sense. When I was teaching and tutoring students, the things that stood out predominantly with people who struggled with math were like a recurring theme in a book. It wasn't always the same struggle, but they centered around a few core struggles. A few of which I noticed in your question.They thought they were bad at math.They wanted shortcuts, not understanding.They thought there was a magic bullet.They had a weak foundation to build upon.They had weak teachers previously.They didn't see any value or need for math.They aren't comfortable with error or the abstract nature of math.You may look at that abbreviated list and think, some of those apply to me. Maybe all of them apply to you, but the danger is thinking those are excuses for why you are bad at math and not obstacles that need overcoming.Additionally, I think we need to refine your goal. You say you want to become good at math.That's admirable, but what does that mean? Do you want to be able to do large sums in your head? Do you want to see new complex math topics and immediately understand them? Do you want to get to a point that you can sit for a test and walk out of the room going, I got a B! I am awesome? Ostensibly, the crux of your question is how do I improve at any task that I set before myself and the answer is always relatively the same framework and it's something I taught while teaching my math students. So that's what I'm going to walk you through as part of my answer. Okay? Great.Step One to Becoming a Math Badass-- Define your goal as a concrete tangible thing.For my students, we started each unit by asking the questions, what should I know how to do by the end of this unit? Then we further defined what that meant. For me, depth of understanding trumps formula application. My tests often featured a problem that we hadn't covered in class, but could be solved using the understanding you developed in class and through homework. If you missed a question, so long as you explained where you went wrong or explained why you went from one step to the next, you got partial credit, because then we could discuss where the logic broke down. Whereas, if you wrote nothing, you got nothing. I didn't care if you got the right answer. A calculator can do the work for you and I allowed the calculator on the test. What was important to me was seeing how you thought through the problem.That seems like I rambled, but there's a reason for it. The goal of becoming a math badass/superhero/high-grade-earner/etc. is different depending on how you define those things. For me, the goal should not be to be good at math, because you can always say I'm not good at math. "I can't apply String Theory. I'm not good at math." You need something that is quantitative in some capacity. I prefer my goal is to increase the depth of my understanding that when confronted with a problem I have never seen before, I can apply the concepts I understand appropriately to solve the problem if it has a solution. But wait, how is that any more quantitative than get good at math Nick? Well, for one, I have a clear measure. It's not my grades, because those are not given quickly enough to be immediate feedback, but rather, I base it on my ability to solve problems I have not faced before that are outside of a problem addressed in the section on graphing slope. This necessarily implies, you are going to have to practice word problems and beyond the assignments, but we'll get there.Step Two to Becoming a Math Badass-- Change the Way You StudyWhat you are currently doing doesn't work. Or your grades would be awesome, so you need to change. But how? There are lots of methods. If you google the topic and end up at Wikihow, I'm sorry. I don't want you to do that, because I feel it lacks some substance. So I'm going to provide an example of what I did, but first, let's identify all the components that come along with studying.Pre-Class Note-takingIn-Class Note-takingReview of Class NotesHomework AssignmentsAdditional ExercisesLet's take them each in turn.Pre-Class Note-TakingI'm a big proponent of the depth method of study known as deliberate practice. As such, a lot of my studying practices are hard. They force you to struggle with the material. I remember sitting at my desk running my hands through my hair, close to tearing it out, because two hours had passed and I was still working on the same problem and it was dinner time. It's uncomfortable. It makes you want to get up and run around or pull out your phone and check Facebook, anything else. But honestly, if your goal is to improve your understanding, you will have to focus, concentrate, and force yourself kicking and screaming through some hardship to learn the fundamentals. Speaking of fundamentalsThe fundamental basis for my system of study is to spend as much time in class focusing on the lecture and asking questions of clarification rather than trying to take notes. Why? Because class is where you can get feedback on your understanding of the material. Most students sit around and take notes. They haven't learnt the material yet. You are using that class time to clarify your understanding because you spent the day before learning the material. You are a step ahead of the class. This means you have to take pre-class notes.I used a variation of the Cornell Note Taking Method. Basically, if you split the paper in half, on the left side, you take notes according to how the book would address a problem as it walked you through the steps. The right side of the paper would be my translating what the book said into pictures and words that made sense to me.For instance,My notes may have been incredibly long, but by the time I was done, I had worked through the problem in words that made sense to me and built a system of logic to solve the problem. (I also used it as an opportunity to positively reinforce my ability to be good at math, because when we go back to review, it's nice to have that reminder that we struggled, but because we are math badasses, we can persevere.) Plus, I used pen. Why? If I made a mistake, I wanted to see it. Writing out your intuitions and mistakes forces you to confront them. It also tells you where to ask questions in class.In-Class Note-TakingNow this is where it's up to you. As I started developing my system it changed, you'll notice there is a blank space at the bottom still. That's where I put my questions and the professors answers. Some problems would get spaced further so I could overlay them in a new color. The purpose of in class notes, as I mentioned earlier, is not to learn the material for the first time, but to clarify what you taught yourself. You want to ask questions. Which means, you'll have to feel stupid for asking something that no one else is asking, but the reason they aren't asking is because your classmates are still learning the material. You understand the material enough that you have questions about it. It's the advantage over the others that you have. Because when they are doing homework later that night, they'll develop their questions and you'll have already addressed them.Review of Class NotesThis is really where I synthesize the two sets of notes I have together. You can set your notes up so that they are synthesized together already if you leave space where you have questions, but I found rewriting the material helped reinforced things for me.HomeworkNow apply what you learned. Again, I used pen. Again, I made note of where my struggles were and why? It's also important to rewrite each step as you do them, because it's reinforcing the process. It's the rote part of learning unfortunately.Additional ExercisesThe professor assigns a few problems from the book. Maybe like 20 in most cases. Something like odds or whatever. I would take the time and do evens as well. One or two additional ones typically to make sure I understood how to solve it. I would focus on doing the gnarliest looking problems too. Like (3(2(x) + 7)^2) - 9 = 0. It's ugly. No one wants to solve that problem, but it is specifically harder for a reason. This is the point of deliberate practice. You keep working on harder problems that make you uncomfortable. Math is fortunate in that, you can tell how difficult something might be based on how ugly it looks the majority of the time. Word problems? Got to do those two. Especially, the full page ones where they tell you that the moon is 7 miles from a comet. But we want to know where the satellite is in relationship to Mars.This isn't the only way by any stretch of the imagination. There are lots of ways. The key take-aways are; highlighting your mistakes, asking questions, and checking for understanding. You'll need to do them all.Step 3 to Becoming a Math Badass-- Practice, Practice, PracticeThis is the part where I tell you, getting good at anything is going to take time. Lots of time. And the question you have to answer is; is it worth it to me? Personally, I think the answer is yes. Math follows a logic that is hard to deviate from. It coaches us through comparisons and finding patterns and deciding whether those patterns are actual patterns or imaginary. It explains relationships between two or more objects and gives you a vocabulary for discussing those differences and similarities. That has incredible value, so in my mind, it's worth learning. But that gets to understanding why you are doing some things when you study. I think practice allows you to keep testing your understanding of the why. Especially, when you are solving problems that are not even in the book (you can find some online or even with a tutor).Some will say you don't need a tutor, you can teach yourself, and it's true, but a tutor is a designated time and accountability measure. Most importantly, they can help you develop practice problems to further test your understanding. You may want to consider it.Step 4 to Becoming a Math Badass-- Rinse, Lather, Repeat.There honestly anything that is secretive or special that will help you. There may be books that you can understand better than others. Check with your professor. The reality, though, is that it will take you many, many hours of effort and work. All skills, no matter what they are, require time and deliberate effort.What I mean is, if you pump weights, but only pump the bar, you will grow in size, but never in strength. It is when you add weights and make it harder, that your strength increases. It's the same with all skills you are trying to develop. You have to practice hard things. Things that are beyond your grasp, but your fingertips are brushing it.It's hard. It's painful. But it's worth it. Being good at math opens a lot of doors to understanding that are normally closed to you if you don't understand it. Not just job careers either. Maybe you'll recognize when a politician is misquoting some numbers and the relationship sounds wildly incorrect.And just to show I'm not a completely horrible human being who didn't really provide you with any secret answers, I'll give you some additional work that I think will help spur you in the right direction.Cal Newport's books talk about hacks for studying, what they are really is time & effectiveness management, but that's important too. You can sample his stuff at his blog. You may want to flip through his archive. http://calnewport.com/blog/To get a practical sense of how people misuse math or misunderstand it and why it's important, I recommend the BBC podcast More or Less. More or Less: Behind the Stats - Downloads - BBC Radio 4Oh and if you want to see where other people misunderstand math. I recommend this list of misconceptions. It might explain concepts that you are personally struggling with. Or things you just go, duh. Count On

If you're looking for reliable statistics on abortion, the best resource to go to is the Guttmacher Institute. They are frequently reviled by staunch pro-life/anti-abortion activists for their leanings & agenda and count Planned Parenthood itself amongst their donors, but no one generally contests their research and data[1] . According to their Induced Abortion in the United States fact sheet:In 2011, 1.06 million abortions were performed, down 13% from 1.21 million in 2008. From 1973 through 2011, nearly 53 million legal abortions occurred.I don't think that Governor Christie was trying to suggest that [math]>2000^3[/math] pregnancies have been terminated. Frankly, I don't think Governor Christie would have even understood that his choice of words might've mathematically suggested an exponent, nor that most of the audience – regardless of partisan alignment or education level – received it that way. He was trying to make the point in dramatic terms that "lots and lots and lots" of pregnancies have ended in abortion over the years. Again citing the Guttmacher fact sheet:Twenty-one percent of all pregnancies (excluding miscarriages) end in abortionAt least half of American women will experience an unintended pregnancy by age 45, and at 2008 abortion rates, one in 10 women will have an abortion by age 20, one in four by age 30 and three in 10 by age 45.If you grant the colloquial use of language, it's difficult to contest Governor Christie's foundational assertion that there have been and continue to be a lot of abortions. The question then becomes, "What does that information mean and how should we respond to it?" And that is where things get heated quickly.I'll set the matter down there, but I encourage people to review the full fact sheet and consider all of the presented information. If any readers want to know where I personally stand, I have other answers on the topic.Footnotes[1] Critical Thinking Resources for Women's Issues