Topic 2 Getting Smarter Through Algebraic Reasoning Answers: Fill & Download for Free

168.That’s how many hours there are in a week.If you’re a student, you probably feel like this isn’t enough. I know … You have so many assignments to do, projects to work on, and tests to study for. Plus, you have other activities and commitments.And I’m sure you want to have a social life, too.Wouldn’t it be nice if you could study smarter (not harder), get good grades, and lead a balanced life?Of course it would. That’s why I wrote this article.The main aim of education isn’t to get straight A’s. But learning how to learn is a vital life skill.So I spent hours scouring scientific articles and research journals to find the best ways to learn more effectively.I’m a lifelong student myself, and I’ve since completed my formal education. Over the course of my academic career, I’ve used almost all the tips outlined in this article, so I can verify that they work.Let’s get started. Here are 20 scientific ways to learn faster.1. Learn the same information in a variety of ways.The research (Willis, J. 2008) shows that different media stimulate different parts of the brain. The more areas of the brain that are activated, the more likely it is that you’ll understand and retain the information.So to learn a specific topic, you could do the following:Read the class notesRead the textbookRead OTHER books on the same topicLook up other online resourcesCreate a mind mapTeach someone what you’ve learnedDo practice problems from a variety of sourcesOf course, you won’t be able to do all of these things in one sitting. But each time you review the topic, use a different resource or method – you’ll learn faster this way.2. Study multiple subjects each day, rather than focusing on just one or two subjects.It’s more effective to study multiple subjects each day, than to deep-dive into one or two subjectsFor example, if you’re preparing for exams in math, history, physics, and chemistry, it’s better to study a bit of each subject every day. This approach will help you to learn faster than by focusing on just math on Monday, history on Tuesday, physics on Wednesday, chemistry on Thursday, and so on.Why?Because you’re likely to confuse similar information if you study a lot of the same subject in one day.So to study smart, spread out your study time for each subject. In so doing, your brain will have more time to consolidate your learning.3. Review the information periodically, instead of cramming.Periodic review is essential if you want to move information from your short-term memory to your long-term memory. This will help you get better exam grades.As the research shows, periodic review beats cramming hands-down.The optimal review interval varies, depending on how long you want to retain the information. But experience – both my own and through working with students – tells me that the following review intervals work well1st review: 1 day after learning the new information2nd review: 3 days after the 1st review3rd review: 7 days after the 2nd review4th review: 21 days after the 3rd review5th review: 30 days after the 4th review6th review: 45 days after the 5th review7th review: 60 days after the 6th review4. Sit at the front of the class.If you get to choose where you sit during class, grab a seat at the front. Studies show that students who sit at the front tend to get higher exam scores. The average scores of students, depending on where they sat in class, are as follows (Giles, 1982):Front rows: 80%Middle rows: 71.6%Back rows: 68.1%These findings were obtained under conditions where the seating positions were teacher-assigned.This means it’s not just a case of the more motivated students choosing to sit at the front, and the less motivated students choosing to sit at the back.By sitting at the front, you’ll be able to see the board and hear the teacher more clearly, and your concentration will improve too.Now you know where the best seats in class are!5. Don’t multitask.The data is conclusive: Multitasking makes you less productive, more distracted, and dumber.The studies even show that people who claim to be good at multitasking aren’t actually better at it than the average person.Effective students focus on just one thing at a time. So don’t try to study while also intermittently replying to text messages, watching TV, and checking your Twitter feed.Here are some suggestions to improve your concentration:Turn off notifications on your phonePut your phone away, or turn it to airplane modeLog out of all instant messaging programsTurn off the Internet access on your computerClose all of your Internet browser windows that aren’t related to the assignment you’re working onClear the clutter from your study area6. Simplify, summarize, and compress the information.Use mnemonic devices like acronyms, as these are proven to increase learning efficiency.Example #1If you want to memorize the electromagnetic spectrum in order of increasing frequency, you could use this acronym/sentence:Raging Martians Invaded Venus Using X-ray Guns(In order of increasing frequency, the electromagnetic spectrum is: Radio, Microwave, Infrared, Visible, Ultraviolet, X-rays, Gamma rays.)Example #2Question: Stalactites and stalagmites – which ones grow from the top of the cave and which ones grow from the ground?Answer: Stalactites grow from the top, while stalagmites grow from the ground.Study smart by using mnemonic devices whenever possible. In addition, you could summarize the information into a comparison table, diagram, or mind map.These tools will help you learn the information much faster.7. Take notes by hand, instead of using your laptop.Scientists recommend this, and not just because you’re more likely to give in to online distractions when using your laptop. Even when laptops are used only for note-taking, learning is less effective (Mueller, P. 2013).Why?Because students who take notes by hand tend to process and reframe the information. In contrast, laptop note-takers tend to write down what the teacher says word-for-word, without first processing the information.As such, students who take notes by hand perform better in tests and exams.8. Write down your worries.SaveWill I do well on this exam?What if I forget the key concepts and equations?What if the exam is harder than expected?These kinds of thoughts probably run through your head before you take an exam. But if these thoughts run wild, the accompanying anxiety can affect your grades.Here’s the solution …In one experiment,researchers at the University of Chicago discovered that students who wrote about their feelings about an upcoming exam for 10 minutes performed better than students who didn’t. The researchers say that this technique is especially effective for habitual worriers.Psychologist Kitty Klein has also shown that expressive writing, in the form of journaling, improves memory and learning.Klein explains that such writing allows students to express their negative feelings, which helps them to be less distracted by these feelings.To be less anxious, take 10 minutes and write down all the things related to the upcoming exam that you’re worried about. As a result of this simple exercise, you’ll get better grades.9. Test yourself frequently.Decades of research has shown that self-testing is crucial if you want to improve your academic performance.In one experiment, University of Louisville psychologist Keith Lyle taught the same statistics course to two groups of undergraduates.For the first group, Lyle asked the students to complete a four- to six-question quiz at the end of each lecture. The quiz was based on material he’d just covered.For the second group, Lyle didn’t give the students any quizzes.At the end of the course, Lyle discovered that the first group significantly outperformed the second on all four midterm exams.So don’t just passively read your textbook or your class notes. Study smart by quizzing yourself on the key concepts and equations. And as you prepare for a test, do as many practice questions as you can from different sources.10. Connect what you’re learning with something you already know.In their book, Make It Stick: The Science of Successful Learning, scientists Henry Roediger III and Mark A. McDaniel explain that the more strongly you relate new concepts to concepts you already understand, the faster you’ll learn the new information.For example, if you’re learning about electricity, you could relate it to the flow of water. Voltage is akin to water pressure, current is akin to the flow rate of water, a battery is akin to a pump, and so on.Another example: You can think of white blood cells as “soldiers” that defend our body against diseases, which are the “enemies.”It takes time and effort to think about how to connect new information to what you already know, but the investment is worth it.11. Read key information out loud.Studies have been conducted, which demonstrate that reading information out loud helps students to learn faster than by reading silently (MacLeod CM, 2010 & Ozubko JD, 2010).What’s the reason for this?When you read information out loud, you both see and hear it. On the other hand, when you read information silently, you only see it.It isn’t practical to read every single word of every single set of notes out loud. That would take way too much time.So here’s the process I recommend:Step 1: As you read your notes, underline the key concepts/equations. Don’t stop to memorize these key concepts/equations; underline them and move on.Step 2: After you’ve completed Step 1 for the entire set of notes, go back to the underlined parts and read each key concept/equation out loud as many times as you deem necessary. Read each concept/equation slowly.Step 3: After you’ve done this for each of the underlined key concepts/equations, take a three-minute break.Step 4: When your three-minute break is over, go to each underlined concept/equation one at a time, and cover it (either with your hand or a piece of paper). Test yourself to see if you’ve actually memorized it.Step 5: For the concepts/equations that you haven’t successfully memorized, repeat Steps 2, 3, and 4.12. Take regular study breaks.Taking regular study breaks enhances overall productivity and improves focus (Ariga & Lleras, 2011).That’s why it isn’t a good idea to hole yourself up in your room for six hours straight to study for an exam. You might feel like you get a lot done this way, but the research proves otherwise. So take a 5- to 10-minute break for every 40 minutes of work.I recommend that you use a timer or stopwatch to remind you when to take a break and when to get back to studying.During your break, refrain from using your phone or computer, because these devices prevent your mind from fully relaxing.13. Reward yourself at the end of each study session.Before starting a study session, set a specific reward for completing the session. By doing this, you’ll promote memory formation and learning (Adcock RA, 2006).The reward could be something as simple as:Going for a short walkEating a healthy snackListening to your favorite musicStretchingDoing a couple of sets of exercisePlaying a musical instrumentTaking a showerReward yourself at the end of every session – you’ll study smarter and learn faster.14. Focus on the process, not the outcome.Successful students concentrate on learning the information, not on trying to get a certain grade.Stanford psychologist Carol Dweck’s research shows that these students …Focus on effort, not the end resultFocus on the process, not on achievementBelieve they can improve – even in their weak subjects – as long as they put in the time and hard workEmbrace challengesDefine success as pushing themselves to learn something new, not as getting straight A’sNot-so-successful students tend to set performance goals, while successful students tend to set learning goals.What’s the difference between these two types of goals?Performance goals (e.g. getting 90% on the next math test, getting into a top-ranked school) are about looking intelligent and proving yourself to others.In contrast, learning goals (e.g. doing three algebra problems every other day, learning five new French words a day) are about mastery and growth.Most schools emphasize the importance of getting a certain exam score or passing a certain number of subjects. Ironically, if you want to meet – and surpass – these standards, you’d be better off ignoring the desired outcome and concentrating on the learning process instead.15. Drink at least eight glasses of water a day.You probably think you drink enough water, but studies show that up to 75% of people are in a chronic state of dehydration.Dehydration is bad for your brain – and your exam grades too.University of East London researchers have found that your brain’s overall mental processing power decreases when you’re dehydrated (Edmonds, C. 2013).Further research has shown that dehydration even causes the grey matter in your brain to shrink.The simple solution?Drink at least eight glasses of water a day. Bring a water bottle wherever you go, and drink water before you start to feel thirsty.And if you’re taking an exam, bring a water bottle with you. Every 40 minutes or so, drink some water. This will help you stay hydrated and improve your exam performance. Plus, this also acts as a short break to refresh your mind.16. Exercise at least three times a week.Exercise is good for your body. It’s also very good for your brain.Various studies have shown that exercise …Improves your memoryImproves your brain functionReduces the occurrence of depressionHelps to prevent diseases like diabetes, cancer, and osteoporosisEnhances your sleep qualityReduces stressImproves your moodExercise is quite the miracle drug!So to study smarter, exercise at least three times a week for 30 to 45 minutes each time. You’ll be healthier and more energetic, and you’ll remember information better too.17. Sleep at least eight hours a night, and don’t pull all-nighters.“There’s just so much to do,” I hear students say, again and again. As a student, sleep often seems more like a luxury than a necessity.But what does the research have to say about sleep?The research shows that if you get enough sleep, you’ll be more focused, you’ll learn faster,and your memory will improve.You’ll also deal with stress more effectively.This is a recipe for excellent grades.So sleep at least eight hours a night. This way, your study sessions will be more productive and you won’t need to spend as much time hitting the books.In addition, sleep expert Dan Taylor says that learning the most difficult material immediately before going to bed makes it easier to recall the next day.So whenever possible, arrange your schedule such that you study the hardest topic right before you sleep.Lastly, don’t pull all-nighters. As psychologist Pamela Thacher’s research shows, students who pull all-nighters get lower grades and make more careless mistakes.18. Eat blueberries.SaveBlueberries are rich in flavanoids, which strengthen connections in the brain and stimulate the regeneration of brain cells.Researchers at the University of Reading have found that eating blueberries improves both short-term and long-term memory (Whyte, A. & Williams, C. 2014).Blueberries may also help to prevent degenerative diseases like Alzheimer’s.19. Eat chicken and eggs.A team of researchers from Boston University conducted a long-term study on 1,400 adults over 10 years. They found that participants who had diets high in choline performed better on memory tests.Choline is the precursor to acetylcholine, which is essential for the formation of new memories.What foods are high in choline?Chicken and eggs (the egg yolk contains 90% of the total choline in the egg).Just in case you’re worried about the high cholesterol content of egg yolks, you can breathe a sigh of relief. Recent studies show that eggs – including the yolk – are a healthy food for just about everyone.And if you’re a vegetarian, there are alternatives to getting choline in your diet:LentilsSunflower seedsPumpkin seedsAlmondsCabbageCauliflowerBroccoli20. Eat omega-3 fatty acids.Omega-3 fatty acids are critical for brain function.One experiment (Yehuda, S. 2005) also found that taking a combination of omega-3 and omega-6 fatty acids reduced test anxiety in students and improved their mental concentration.Omega-3 fatty acids are linked to the prevention of high blood pressure, heart disease, diabetes, arthritis, osteoporosis, depression, attention deficit/hyperactivity disorder (ADHD), dementia, Alzheimer’s, asthma, colorectal cancer, and prostate cancer.That’s an incredible list!Here are foods that are rich in omega-3 fatty acids:SalmonSardinesMackerelTroutFlaxseedPumpkin seedsWalnutsThe bottom lineThis is a long article that contains a lot of information. But don’t feel overwhelmed, because there’s no need to implement everything at one shot.As the saying goes …How do you eat an elephant? One bite at a time.In the same way, to implement all 20 tips in this article, do it one tip at a time. Focus on just one tip a week, or even one tip a month. Once you’ve turned that tip into a habit, move on to the next one.Throughout the process, don’t let the goal of getting straight A’s become an unhealthy obsession. After all, education is about much more than getting good grades.It’s about the pursuit of excellence. It’s about cultivating your strengths. And it’s about learning and growing, so you can contribute more effectively.There’s hard work involved, but I know you’re up to the challenge.

Actually there is!I’m an electrical engineer and the math you have to take to pass those classes are about as brutal as they come. Calculus 1,2,3, Differential Equations, Linear Algebra, Complex Analysis, probability and stochastic processes for scientists and engineers. Diff eqs and complex analysis are perhaps the hardest courses I’ve ever taken.I was never stellar at math through high school, in fact, when I first started college at a community college, I was placed in pre-calculus. For those of you who don’t know, in America unless you pass the entrance exams for Calculus, Physics and Chemistry, you will not go straight into Calculus 1 or Physics 1 or Chem 1A. Basically you have to take remedial classes like pre-calculus or pre-physics or pre-chemistry. Then you wonder why it takes 5–6 years to get through undergrad for basically most engineering majors! Everybody I knew in my EE classes took about 5.5 years because we had to do something like 135 units which was the most for any major at that university.I struggled in the beginning then ‘I thought’ I found out something about myself, which might be one reason some people aren’t good at math. At first I thought I had what is known as:DyscalculiaI used to joke with myself and say, “That means, you can’t do Calculus”. If you laughed at that joke, you are a true geek like me.. just admit it, it’s ok!Actually it means: Difficulty in learning or comprehending arithmetic, such as difficulty in understanding numbers, learning how to manipulate numbers, and learning facts in mathematics. It is generally seen as a specific developmental disorder according to the web.But soon I figured out it was pretty unlikely I had that, if I did it was probably not a significant contributor.After years of self diagnosis and adjustment, I found out a few things but before I tell them to you, I want to discuss why math is feared and why high school and college are actually contributing to what is know as math anxiety.Every math and engineering class I’ve ever taken had the following format.You can follow the textbook roughly and the easy worked out examplesYou can follow the easy examples the prof will do in classYou can manage the homework with some helpBUTThe exams are a completely different story. In exams, this is what happens.They are usually problems you’ve never seen; that is, most of the time you have no clue how to solve it. And if you spend 5 minutes thinking about one problem, you are basically wasting time and you can’t afford to do that.It is speed contest. This is the biggest thing because in most cases you are given way more problems than you can solve in an hour and the person who solves them the fastest and most accurate wins. Speed!The above is what builds what is called math anxiety! This is primarily due to the fact that you have little time to solve huge problems and if you don’t, you get penalized. Once this behavior is learned, students eventually just give up or just say to themselves, “Oh well, I’m not good at math”. So it’s not enough that you can do them, you better be quick at it!So the system is inherently built to scare you with mathematical finesse.I think 50–100 years from now, the system will be much different and the expectations won’t be as crazy. Realistically, once you get out of college, you hardly use any math even in electrical engineering because that’s what computers are for. They model, simulate and calculate circuits, communication systems and all other aspects of engineering better and faster than you can on paper. Honestly, unless you are going to do a PHD or become a professor, you really don’t use all that math once you start working.What worked for me ?First, I tried to understand how I learned. Figure that out first for yourself. Some of us are visual learners, some are auditory learners. Most people have a combination of both. In my case, I was extremely visual to the point where if I couldn’t visualize it, it made no sense to me. This is why I sucked at pure math.What I’m getting at is that, when there is no application, it was hard for me to just solve a problem because I needed to be told, “Why we are doing this and what purpose does it solve?” and obviously no one will answer that. instead you will be given something like the following to evaluate.The above made no sense to me from a pure math point of view. My questions were:What does this represent in the physical world?What does the input and the output mean?What real world problem does this model or solve?Why exactly do you want me to solve this? Other than to just do it.A lot of Calculus and differential equations although some of it is applied, is usually just “solve this or that” because that is what is required. So my biggest problems was, without context to the real world, I had trouble relating.Unfortunately, if you don’t go through the practice of just doing it for the sake of doing it, you will fall behind fast and that’s what happened to me.To me pure math like Calculus 1, 2 and 3 and then differential equations made zero sense because it was mixture of.Do it because we told you so.What math tricks do you recall or know?Showoff your mathematical finesseHow fast can you do it?In essence, it was sort of a discipline where if you know how to crack the system (as most of us have learned either consciously or unconsciously) you were good. That is, you could basically skate through all the way up to diff eq by just knowing a few tricks and not really understanding what was going on. Until of course you were asked to do a math proof where half the class would fail.To get through pure math, I would try to understand the following.Basic math concepts without any math. Even if you are great at math, you’d be surprised at how many things you never knew or missed because you were too busy just plugging in stuff into an equation and solving for speed.Understanding the symbols in math. This was one of my biggest challenges. The math symbols are basically another language and you need to know it to the point where you can decode it. Not understanding the symbols and the language of math is perhaps the biggest contributor to math anxiety.Become a master at arithmetic and algebra. Believe it or not higher math is dependent on and built upon basic skills. For example, one could argue, solving differential equations is simply the use of algebra and basic calculus. In the end, a tiny algebra mistake could cost you half the credit for the problem on a test! It did for me!Understand all the basic math functions. This is important and part of understanding the math language and symbology because you need to know what basic arithmetic, algebraic and transcendental functions do and how to use them and what operations can be used on them. I’m talking about the underlying concept and purpose.keep practicing with homework problems and other problems from the internet or guide books to build speed.After I got through pure math which was a nightmare, I finally started to understand math once we started applying it. I caught onto to math in Physics because it taught me that we can actually model most of the things that happen in nature with math and be pretty accurate. It was intriguing to me that most of the things like a falling body, or a trajectory or planetary motion could all be described using math. We lived in a mathematical world! I almost feel that should have been my first lesson before arithmetic instead of the common rote memorization of arithmetic skills that is encouraged.During my second semester of Physics which was all about Electricity and Magnetism, I totally bombed the first exam and got a D or something but I did okay on the next two exams. When I talked to the professor he said, “Oh I have to think about you. You did bad on the first exam but you got the highest score in the class on the final” and he gave me an A-.Then as I got into more electrical engineering classes, the math got more brutal but what sort of helped me was the following and also a book called, “how to solve it” by George Polya. A classic! In it he talks about things like.Always strip a problem down to its basicsTry to solve it in pieces if you canTry to see if you could solve a lesser problem and build from thereTry to see if you know a trick or something you did in a similar problemAlso, I remember a friend of mine when we took a class titled “Signals and Systems”. By far this is one of the hardest classes you take as a EE. By this point, you pretty much have to know every single math trick you can think of and be ready to use it in your sleep. We were doing Fourier transforms for signals and communications. This was one of those gateway classes that a lot of people did bad on. That is, it really tested you if you were EE material. I noticed my friend was getting all A’s and I asked him, “How are you doing this?”. And he told me, “Oh, I just sort of found a trick to this class!” That is, he saw a similar sort of pattern to solve all those problems. Sometimes it’s all about knowing that math trick or a property you can exploit or sort of anticipating the type of questions the professor might ask and just sort of mastering those skills.I hope the long explanation above helped. I personally think everybody is capable of learning math but you have to find out how you learn and exploit it to your best ability and put in the time to understand it. Don’t worry about how fast somebody else can solve a problem, you goal should be to understand for yourself no matter how long it takes. Good luck!EDIT - Some more information.A few of you asked me where to find a list of basic concepts. Well that’s the hard part. The problem is that you have to hunt around the internet for a pre-made list or find a book that might talk about the conceptual aspect of math instead of speaking to you directly in math symbology. Or you have to get a list of things you should know and do extensive google search on each topic and make your own notes. I did find a simple document from the University of Ithaca, NY. It may seem like this is something that your high school teacher would pass out but honestly this is the type of stuff you need to understand. For example, even at my level, there were one or two things I never knew and I’m not ashamed to admit it! That is, I found myself saying, “Oh I never thought about it that way!” Take a look at this link for 12 basic math concepts you probably picked up in high school. You should really know this before going into pre-calculus. The main problem with math is professors usually gloss over the conceptional explanation and just start using symbols, equations and proofs. Bottom line is that you need to speak the math language. Literally what that means is that just like you are reading the words on this post, you need to decode math symbology quickly. Hopefully the link stays up. Thanks!https://faculty.ithaca.edu/novak/docs/Twelve_Concepts.pdf

Disclaimer: I'm not a physics Ph.D student, but I spent a long time researching the career path of one interested in particle physics since I myself wanted to pursue a research position. If another person with the credentials posts an answer, of course you should probably defer to them first.Usually in physics, the standard procedure is to graduate and do a post-doctoral appointment, which is a 1-3 year contract that is sort of like residency for medical students. It's meant to help you transition from a doctoral student making his first major independent contribution to a researcher that can do this regularly and more efficiently. You're probably looking at trying to be a professor, research scientist, or somewhere in industry.Most will do at least one postdoc before they can reasonably expect a tenure-track position (and usually you'd have to do more than one, unless you've done some really good work). Some people say that once you get past three postdocs, you're unlikely to land a favorable academic position. In other fields, people can apply to tenure-track positions right after Ph.D or after their first postdoc, and I think the reason for the differences is simply because there are supply and demand forces going on. Particle physics, string theory, cosmology, and other very sexy but esoteric fields will be quite competitive because that's what sells books and gets good ratings when Morgan Freeman is doing his best Carl Sagan spiel. Anyway, you want to make sure that you do work that is really good and makes big impact, and you want everyone to know about it.That last point is crucial actually. I've said this before in some of my other posts. As much as people would like to think so, academia is not a meritocracy. You'll have to sell yourself just like in any other field, but in a different way. That means building your connections, being associated with high profile people and institutions, and doing high profile work. If your Ph.D advisor won a Nobel prize, you're in a good position. If your work has hundreds of citations by the time you're looking for positions, you're doing well. If you have friends in many places that can personally recommend you for a job (so that you're not just another CV in a pile of hundreds), then you're doing well. If you know people on the grant review committee or publication review committee, you're going to have an easier life. It's really not much different than trying to get a normal job, except that it's more complicated and uncertain. Your closest industry brethren are probably salesmen, actually.That being said, sometimes even all of that isn't enough. Making it in academia gets harder at each step. Think about it this way. In high school, you were vying for the top colleges. Then you have to apply to graduate school. If you were at Caltech, got a good GPA and did a little research for a summer, sometimes that will be good enough to get into a top graduate program. If you went to a state school, you will have to do a lot to get on the same level as the Caltech guy, because names unfortunately do matter. They are not the end of the story, however. Amazing people will get into the top schools regardless of where they're coming from because of their accomplishments, but you have to make sure you're making visible accomplishments. Anyway, on to the next step. You're at a top institution. If you're not, the one way I can think of that still keeps you competitive (with a reasonable chance of success) is that you can get a high profile advisor. In these cases, advisor will trump school almost always. But obviously you're more likely to find someone good if you're at a top school.Now there's the next level of competition: postdocs. This gets stiffer because not only are you competing with your classmates at your own school and other top schools, but you're competing with people who already have one or two postdocs (and sometimes more) under their belt. There are not enough positions to go around for everyone, so inevitably some people will end up being pushed out of academia. This is a situation I'll come back to later, but it's very important. Once you get to the point where you're going to start applying for positions, competition will be even more stiff (partly because grad students and postdocs are much cheaper than professors..and ones that you'll be giving tenure so you're stuck with them). Tenure review comes up a few years after you've been at the institution for a while. Some people won't make tenure the first time, so they'll try another tenure-track position. It's pretty volatile.Let's put some things into perspective. You started college at 18, finished at 22, and took 6 years for your Ph.D, so you're 28. Then you do 2 postdocs, each averaging about 2 years each, so that puts you at 32. Then you come up for tenure review and don't make it, so that's.. maybe 3 years gone? Another 3 years and, thank goodness, you made tenure. You're 38. Wow. Depending on where you are geographically, your salary will be between $60,000 and something like $100,000. Before that, your postdoc positions might pay you something like $50,000. Grad students are lucky to get $30,000. You've lost quite a bit of money, and this assumes that everything went right at each stage. That you were the lucky 10%--not top 10%, just lucky 10%.So what happens if something goes wrong? Well, I think if you look up the stats, you'll find that it's very likely you won't make it to the next step. Take a look at this link:http://particle.physics.ucdavis.edu/rumor/doku.php?id=where_are_theyThis is from what's called the particle physics rumor mill, where 'rumors' about job offerings and who will get them go around. They have a page, which I've linked, that also tells where some of the promising people went off to when they kicked the academic career path bucket. One guy, Jorge Lopez, has over 3000+ citations, and now works for Shell. Now, he's just one data point, and we don't know his personal case. He might have gotten burned out, tired of not making money, or quit even though he had tenure. But there are a lot of people on that list, and I'm willing to put a large amount of money on the line to say that these are people who didn't make it to the next level. Instead, they went to Wall St., oil and gas, high tech, national lab, or software.This part is important. The only reason these people got jobs at industrial labs like this is because of an obvious point: those companies needed them to do something. Unfortunately, this is an obvious point lost on a lot of pie-in-the-sky Ph.D students (and not just physics). If you did string theory, you are probably extremely good at math. Wall street loves these guys, but they need to know finance. If you can't pick up a stack of finance books and work through them enough to show your interviewer that you are teachable and willing to learn, you're not getting anywhere near that job. If you're interviewing at Google and all you've ever written is FORTRAN code with goto's, wrote a few HTML pages for your research, and never heard of version control, you have no chance. If you did experimental research in superconductors, but you don't know the basics of computer architecture, no industrial electronics lab is going to want you. The only exceptions are when they basically have no one else they can turn to, a la Wall St. in the 80s and 90s where they would snatch up math, physics, and engineering Ph.D's like it was nothing. But that's a supply and demand thing, so you'll have to be careful and be sure you understand the market. I've read about physics Ph.D's tending bar, working in insurance, waiting tables, or something of the sort because they can't find a job and their field of study just wasn't relevant in industry, or they didn't develop marketable skills. Entry level engineering positions are off the table since Ph.D's are too expensive and there's no guarantee that they won't run away once they get bored and find a better position. In a lot of "lesser" jobs or careers, managers will not want people who are way smarter than them either. That's a social issue that has to be understood. There are more examples of these issues (practical and social), but I think I've made my point.So what should be taken away from this rather cynical post? Develop marketable skills. Keep a side interest in your plan B. Know your way out, because it's very likely that you'll need to. Read a software design book. Try to learn some high performance computing tips when you're working on simulations. Try to work in an experimental lab that will have applications beyond just research, and know the stats for the market you're looking at. I have to say something about this last point: so many people capable of doing quantum field theory and Lie algebra can't do their diligence on finding out actual statistics for jobs. It's bizarre. Don't just trust what people say, especially your professors. They most likely don't know anything about industry, they've spent their entire lives in academia! Don't blindly go for the sexy stuff just because you want to be the next Einstein, because in most cases, it's not going to happen. That's not to say that you shouldn't try, but make sure that you're doing what you need to do to put food in your mouth (and your wife's or children's, if you have any, and chances are that by the time you're 38ish, you will). If you want to do astrophysics, fine, but do a computational topic and learn to write good software, algorithms, and know some HPC. You can do particle physics, perhaps quantum chromodynamics where it's a highly computational field as well. Do thin film superconductors so you can go work at HP labs or something. Solid state physics uses the same math as particle physics, but they do useful stuff (e.g. materials, electronic structure, scattering). If you're doing big bang cosmology, just brush up on your CFD so you might be good to work at a fusion lab or modeling oil flows for an oil company. And if you're doing experimental particle physics, learn how to build and engineer accelerators, or look into medical physics.I didn't talk much about national lab positions, because they're pretty hard to get as well, but the path to it is the same. Network the shit out of everyone. Make sure your research is relevant to the people and the institution. Demonstrate that you can bring in funding. Get known within your scientific community. Etc.Hope this helps. If you want to continue reading about the perils of getting a Ph.D in physics, follow these links as they were extremely helpful to me.http://physicsforums.com/forumdisplay.php?f=139&daysprune=-1&order=desc&sort=replycounthttp://physicsforums.com/forumdisplay.php?f=193&daysprune=-1&order=desc&sort=replycountAnyway, take all this information and consider it. In the end, it still might be worth it to you. For me, I realized that it was not, and I've changed my direction towards computer science instead so I can more easily do research in industry. Lots of people still continue on to do physics and become successful, but just understand the statistics behind these situations. You don't take anyone's word on what the nature of reality and the universe is like, so don't take anyone's word on what your future is going to be like. Don't be ignorant, do your research.