Asking for Ye ole Guidance and Opinion

[gohabsgo]

I'm a recent History degree graduate with about a year or two to spare before I enter law school. I'm still very young, being fresh out of the university, but find I have nothing really to do with my time. (A current situation has forced me to spend more time helping out family members, barring me from getting a job and also entering law school at an ideal time.) That said, I've wanted to learn Algebra, something that I was exempt from in college because I barely managed a B in a high school college accredited Trigonometry course. I never performed well in any of my math courses in high school because I simply never completed the homework. I basically scraped by with Bs at the end of semesters, all the way through my high school's College Algebra course. Anyways, as I've said, I want to start my journey through Algebra, actually learning it this time, so that I may unlock other aspects of mathematics and science. To be honest though, I'm nervous to purchase a book on algebra for fear that I may not understand or be able to self-teach myself the concepts. Throughout my life I've had an ever-present fear of math, but I want to finally overcome this.

I was thinking of possibly getting the Algebra and Algebra 2 for Dummies series, along with their workbooks before getting a college-level text on the same subject. I've also never been strong at word problems at all, and ask if any of you have a brilliant text to remedy that. But if I were to get the said "dummies" books and used those to progress, would I be able to possibly pick up on the concepts quickly and efficiently? My ultimate goal is to possibly reach or complete up through Calculus 1 on my own, in a year's time. Would this even be possible? Have any of you took up a self-teaching journey even though you're not the strongest mathematical mind?

I guess I'm getting long-winded. I've already looked ahead at some college-level texts such as College Algebra by Blitzer, but do ask for any other recommendations. I do realize that there are many online resources, but I prefer a physical book with which to complete my studies.

Finally, I'm a calculator kid. Is that a bad thing? I guess I mean that I've always used a calculator since entering Algebra 1, but notice that now many of my contemporaries are being forced to use their mental capabilities for some of their Algebra. Hell, a Calculus teacher at my university barred calculators because of some mental method he created. I guess I'm asking if I need to be mathematically gifted and refrain from always using a calculator, or maybe that doesn't really matter at all. Anyways, this is all I have for now, and ask for any guidance or opinions I can get.

 

[chiro]

Hey there and welcome to the forums

First thing about learning: there are many different ways to learn both by yourself and in a more social environment. Some people can teach themselves almost anything and have a strong drive to learn by themselves, but most people do not.

One of the things about a social learning environment (like a high school, community college, university) is that its a lot easier to learn. Its a lot easier for most people to go to a lecture, sit down absorb as much as they can, maybe form a study group with other like minded people and more motivated than someone who spends a lot of time in isolation. In fact I think you'll find that a lot of universities try and encourage the social aspect very strongly as it can be a factor in determining how successful people are with learning and their GPA.

However, if you are a type of person that wants to learn no matter what, you will probably succeed whether in isolation or by yourself.

If you do want to go through the self-learning route that's great and I wish you all the best. If you get stuck you could use these forums to get around the headaches that you may come across in math. Math is unfortunately (and fortunately depending on your perspective) one of those subjects that cause a lot of headaches for a lot of people. Some people can see things in a way that are really brilliant and others struggle just to get the basic idea.

Now I hear a lot from people that you should stick with only what you're good at. I think this is absolute nonsense. If you want to learn something and got off on the wrong foot, keep trying because as long as you improve consistently, you will become good. If everyone stopped doing something because they had a setback we would still be living in the stone-age.

Also about being a "calculator kid". Most people that have studied math for a long time will see math differently than those who have only done math in primary and secondary high school.

To me math is about two things: being as broad as possible and then being specific. I'll give you an example:

Lets look at numbers. First you learn about positive whole numbers. You learn about addition and multiplication of these. Then you look at negative whole numbers and you learn about subtraction. Then you learn about fractions and learn about division.

Finally you learn about all these "inbetween" numbers that aren't normal rational numbers (example a/b where a and b are whole numbers and b != 0).

Then if you're lucky you learn about complex numbers.

In the above example each step generalizes everything before it. So we started at whole numbers and worked our way up to real numbers and complex numbers. Thats what I mean about being broad.

So once we have gotten "broad", mathematicians try and find out things about the broadest thing possible and then when they can prove whatever they are trying to prove.

Then about 10-20 years goes by and a scientist will run into a problem and they will see that this mathematician found something out and they will use it in a more specific problem they are trying to solve.

The pure math guys usually work on the "broad" stuff finding things out that cover a lot of different scenarios and find and prove things that are most likely going to be useful for other scientists. The applied guys use what the pure guys have done and apply it to something specific.

I guess what I'm trying to say is that math is not about calculating stuff and its not even about greek letters and algebra: its about looking at different areas from a "broad" view and then seeing what the consequences are for "specific" things.

I hope that helps!

 

[gohabsgo]

Hey there and welcome to the forums

First thing about learning: there are many different ways to learn both by yourself and in a more social environment. Some people can teach themselves almost anything and have a strong drive to learn by themselves, but most people do not.

One of the things about a social learning environment (like a high school, community college, university) is that its a lot easier to learn. Its a lot easier for most people to go to a lecture, sit down absorb as much as they can, maybe form a study group with other like minded people and more motivated than someone who spends a lot of time in isolation. In fact I think you'll find that a lot of universities try and encourage the social aspect very strongly as it can be a factor in determining how successful people are with learning and their GPA.

However, if you are a type of person that wants to learn no matter what, you will probably succeed whether in isolation or by yourself.

If you do want to go through the self-learning route that's great and I wish you all the best. If you get stuck you could use these forums to get around the headaches that you may come across in math. Math is unfortunately (and fortunately depending on your perspective) one of those subjects that cause a lot of headaches for a lot of people. Some people can see things in a way that are really brilliant and others struggle just to get the basic idea.

Now I hear a lot from people that you should stick with only what you're good at. I think this is absolute nonsense. If you want to learn something and got off on the wrong foot, keep trying because as long as you improve consistently, you will become good. If everyone stopped doing something because they had a setback we would still be living in the stone-age.

Also about being a "calculator kid". Most people that have studied math for a long time will see math differently than those who have only done math in primary and secondary high school.

To me math is about two things: being as broad as possible and then being specific. I'll give you an example:

Lets look at numbers. First you learn about positive whole numbers. You learn about addition and multiplication of these. Then you look at negative whole numbers and you learn about subtraction. Then you learn about fractions and learn about division.

Finally you learn about all these "inbetween" numbers that aren't normal rational numbers (example a/b where a and b are whole numbers and b != 0).

Then if you're lucky you learn about complex numbers.

In the above example each step generalizes everything before it. So we started at whole numbers and worked our way up to real numbers and complex numbers. Thats what I mean about being broad.

So once we have gotten "broad", mathematicians try and find out things about the broadest thing possible and then when they can prove whatever they are trying to prove.

Then about 10-20 years goes by and a scientist will run into a problem and they will see that this mathematician found something out and they will use it in a more specific problem they are trying to solve.

The pure math guys usually work on the "broad" stuff finding things out that cover a lot of different scenarios and find and prove things that are most likely going to be useful for other scientists. The applied guys use what the pure guys have done and apply it to something specific.

I guess what I'm trying to say is that math is not about calculating stuff and its not even about greek letters and algebra: its about looking at different areas from a "broad" view and then seeing what the consequences are for "specific" things.

I hope that helps!

Well said chiro and thanks for your response. You're definitely right about the social setting. I would prefer that over solitary learning, but unfortunately I cannot partake in any of those settings due to my current situation. I definitely see your response as inspiration and will use it as so. Thanks again!

 

[chiro]

It is unfortunate about the finances required to get an education nowadays. I assume you're from the states. When I found out how much it costs to get an education, I was shocked to hear some tuition rates are as high as 50,000 dollars a year. Its absolutely nuts. I'm surprised you guys haven't started a revolution to get fair access to education.

I will still suggest that you can use the internet and find plenty of resources, and if you're stuck come to a forum (this or another one) and post a question. Most people here are very bright, very knowledgeable, and very friendly in my experience. As long as you put in an effort and do your best to outline specifically what you're not getting and put the appropriate context in your question so that we can help you, people here will more than likely give you a nudge in the right direction.

One thing you should never do (either here, a university, or in a job) is to ask for help without putting in prior effort to understand. If you do that people will not be inclined to help you and may tell you straight up what they are thinking (and its not going to be good).

Maths is kinda weird because there is a somewhat larger than normal probability of people that have some kind of mental condition whether its schizophrenia, bipolar, high functioning autism, and with this you get some people who are a bit eccentric, highly socially withdrawn yet very brilliant and insightful when it comes to science and/or mathematics.

Just with regard to your law degree, there was a document I read a while ago that said that the people that got the highest LSAT scores were the students that came from physics and mathematics. I would give you the link but I saw it so long ago that I forget the original source (Someone linked to it on a thread in this forum so you could try searching for it)

Things that might help you may include logic and statistics. The kind of reasoning in those two areas can help you look at analyzing problems and also help you to identify steps when you need to construct a clear argument. My guess is that your history degree asked you to do this but it can't hurt to see how mathematicians do it at least at the basic level.

If you do the above you don't have to look at a rigorous math book with proofs everywhere: just find a conversational book outlining what stats and logic is all about without using greek symbols everywhere to explain something that could have been said in a few lines. The "for dummies" series might have such a book but I don't agree that the readers themselves are actually "dummies", to me that is too condescending.

 

[CRGreathouse]

When I found out how much it costs to get an education, I was shocked to hear some tuition rates are as high as 50,000 dollars a year.

It would be hard to find a place charging that much. What most people actually pay in the US is about $10,000 to $20,000 per year.

 

[Grep]

I never performed well in any of my math courses in high school because I simply never completed the homework. I basically scraped by with Bs at the end of semesters, all the way through my high school's College Algebra course. Anyways, as I've said, I want to start my journey through Algebra, actually learning it this time, so that I may unlock other aspects of mathematics and science. To be honest though, I'm nervous to purchase a book on algebra for fear that I may not understand or be able to self-teach myself the concepts. Throughout my life I've had an ever-present fear of math, but I want to finally overcome this.

First of all, it's great that you want to do this! There's really nothing to fear in math. And unless you pick up a really advanced book, you should be fine. Algebra isn't really that hard, once you get into it.

Time to torture a metaphor. Math is like a pyramid. You can't build the second layer of stones until you have a good solid first layer (and can't build the third without the second, etc). I've noticed so many people go off course early on by not understanding some key concepts. They have little to no hope of ever understanding things later on without that foundation. So they fall back on rote memorization. A very, very bad idea. I'd probably hate math too if I had to memorize all that stuff.

So make sure you start really simple and understand everything before moving on. I wouldn't be seen dead with a "for Dummies" book, but to be honest, they're usually pretty darn good. I'd suggest the textbook I use, but it's from College a long time ago and I don't know if it's even in print. Textbooks are usually the best, in my opinion. For one, they have enough exercises in them. The downside is they're criminally expensive these days.

Lots of exercises is critical. You need to practice. You noticed not doing all your homework didn't work so well before, right? :)

I was thinking of possibly getting the Algebra and Algebra 2 for Dummies series, along with their workbooks before getting a college-level text on the same subject. I've also never been strong at word problems at all, and ask if any of you have a brilliant text to remedy that. But if I were to get the said "dummies" books and used those to progress, would I be able to possibly pick up on the concepts quickly and efficiently? My ultimate goal is to possibly reach or complete up through Calculus 1 on my own, in a year's time. Would this even be possible? Have any of you took up a self-teaching journey even though you're not the strongest mathematical mind?

Well, I'm not a great example since I was always pretty good at math. In part, I think, because I always insisted on actually understanding stuff. I hate rote memorization. But in my opinion, yes, it's possible to get through up to Calc 1 inside of a year. I'm quite sure of it. But we're talking a whole lot of work, here. I advise not trying to race through it too much at the expense of understanding. I suggest you work through it at your pace, and don't worry too much about where you end up.

Finally, I'm a calculator kid. Is that a bad thing? I guess I mean that I've always used a calculator since entering Algebra 1, but notice that now many of my contemporaries are being forced to use their mental capabilities for some of their Algebra. Hell, a Calculus teacher at my university barred calculators because of some mental method he created. I guess I'm asking if I need to be mathematically gifted and refrain from always using a calculator, or maybe that doesn't really matter at all. Anyways, this is all I have for now, and ask for any guidance or opinions I can get.

Here is where I suspect many people will disagree. I'm of two minds on the calculator thing. On one hand, the ability to do efficient hand calculation on paper isn't as important as it used to be, I suppose.

On the other hand, I would personally make sure you can do your calculations by hand, on paper, if you need to. Kind of sad to be completely lost without a calculator, in my opinion. More than that, I think working with the numbers on paper and in your head gives you a better feel for the way numbers work.

I don't even use paper anymore to add or subtract 3-4 digit numbers. I can do it in my head, and so could you if you learned how. Also getting good at squaring numbers up into the 20s in my head. Next up is learning to multiply in my head. It's surprising how easy it is to learn to do these things. You don't need to be a math genius to do a lot in your head, and even less to do it on paper. And it's kind of fun, and seems to impress people. It's not strictly necessary, but it's simpler than you think. So don't be scared off it if you are interested. Which reminds me, make sure you know your multiplication tables backwards and forwards! If you have to pick up the calculator to figure out "6x7", that's not good.

But all you really need to be able to do is to work it out on paper, if you need to, without being super rusty at it. Not hard. We're talking adding, subtracting, multiplying and dividing, and knowing your multiplication tables. That's all. At worst, practice it from time to time so you don't forget how to do long division, or how to handle decimals.

However, I should mention that in exams, SATs, and such, I suggest always using a calculator. And sometimes, you just need the calculator anyway (like for sines).

I'll leave textbook recommendations to people who know more about the current batch, but one old but excellent math book is "Math for the Million" by Lancelot Hogben. It's probably cheap, and it's pretty easy to understand. Even gets into Calculus near the end. Only problem is there's not enough exercises, I think. But other than that, a generally well regarded book. Not important, but I got a kick out of the testimonial on the back:

"It makes alive the contents of the elements of mathematics." - Albert Einstein

Also, when you get to Calculus, James Stewart's "Calculus" is pretty good, and seems to be quite popular. There are much easier books for Calculus, but it's thorough and quite good, in my opinion.

Hope that helps a bit. I'm sure there's differing points of view on what I've said, but it's what I've found to be the best so far, in my limited experience.

P.S. Good thing I save my posts before I submit. Of course, PF would become inaccessible as I write a really long forum post. Glad I didn't lose it after all that typing.

 

[The_Duck]

I guess I'm asking if I need to be mathematically gifted and refrain from always using a calculator, or maybe that doesn't really matter at all.

In algebra and beyond, a calculator isn't helpful for most of the things you're learning. You're playing with equations instead of doing arithmetic, and most calculators can't do this. Advanced calculators and computer programs can, but you shouldn't use these as it defeats the whole point. And doing this math without a calculator doesn't require you to be "mathematically gifted" at all.

For example in algebra you learn how to solve equations like x^2 - 2x + 1 = 0 for x. A basic calculator helps you not at all with this problem. You could plug this into a TI-89 or something and get the solution x = 1. But in doing so you learn absolutely nothing about the methods for solving these equations, which is the point of the exercise.

 

[Angry Citizen]

I'll echo that sentiment. I rarely need a calculator in my calculus classes, and that's just for computing approximations like the occasional integral using Simpson's Rule (I never trust my head math). Even still, you learn to approximate things mentally, like saying pi/3 is a little over 1. Math, from what I've seen, is more about noticing when you're wrong than figuring out what's right. Then again, this is an engineering student's perspective.

 

[djosey]

Two words for you: Khan Academy. I know you said you wanted a real book and not an online ressource, but i'd still advise you to look at the website, I've found it great for a not scary introduction to maths.

 

[Quark_Chowder]

I'm a recent History degree graduate with about a year or two to spare before I enter law school.

I've also never been strong at word problems at all, and ask if any of you have a brilliant text to remedy that.

You're a LAW student and you can't do word problems? Seriously? They're rarely anything more than logic problems...

 

[gohabsgo]

First of all, it's great that you want to do this! There's really nothing to fear in math. And unless you pick up a really advanced book, you should be fine. Algebra isn't really that hard, once you get into it.

Time to torture a metaphor. Math is like a pyramid. You can't build the second layer of stones until you have a good solid first layer (and can't build the third without the second, etc). I've noticed so many people go off course early on by not understanding some key concepts. They have little to no hope of ever understanding things later on without that foundation. So they fall back on rote memorization. A very, very bad idea. I'd probably hate math too if I had to memorize all that stuff.

So make sure you start really simple and understand everything before moving on. I wouldn't be seen dead with a "for Dummies" book, but to be honest, they're usually pretty darn good. I'd suggest the textbook I use, but it's from College a long time ago and I don't know if it's even in print. Textbooks are usually the best, in my opinion. For one, they have enough exercises in them. The downside is they're criminally expensive these days.

Lots of exercises is critical. You need to practice. You noticed not doing all your homework didn't work so well before, right? :)Well, I'm not a great example since I was always pretty good at math. In part, I think, because I always insisted on actually understanding stuff. I hate rote memorization. But in my opinion, yes, it's possible to get through up to Calc 1 inside of a year. I'm quite sure of it. But we're talking a whole lot of work, here. I advise not trying to race through it too much at the expense of understanding. I suggest you work through it at your pace, and don't worry too much about where you end up.Here is where I suspect many people will disagree. I'm of two minds on the calculator thing. On one hand, the ability to do efficient hand calculation on paper isn't as important as it used to be, I suppose.

On the other hand, I would personally make sure you can do your calculations by hand, on paper, if you need to. Kind of sad to be completely lost without a calculator, in my opinion. More than that, I think working with the numbers on paper and in your head gives you a better feel for the way numbers work.

I don't even use paper anymore to add or subtract 3-4 digit numbers. I can do it in my head, and so could you if you learned how. Also getting good at squaring numbers up into the 20s in my head. Next up is learning to multiply in my head. It's surprising how easy it is to learn to do these things. You don't need to be a math genius to do a lot in your head, and even less to do it on paper. And it's kind of fun, and seems to impress people. It's not strictly necessary, but it's simpler than you think. So don't be scared off it if you are interested. Which reminds me, make sure you know your multiplication tables backwards and forwards! If you have to pick up the calculator to figure out "6x7", that's not good.

But all you really need to be able to do is to work it out on paper, if you need to, without being super rusty at it. Not hard. We're talking adding, subtracting, multiplying and dividing, and knowing your multiplication tables. That's all. At worst, practice it from time to time so you don't forget how to do long division, or how to handle decimals.

However, I should mention that in exams, SATs, and such, I suggest always using a calculator. And sometimes, you just need the calculator anyway (like for sines).

I'll leave textbook recommendations to people who know more about the current batch, but one old but excellent math book is "Math for the Million" by Lancelot Hogben. It's probably cheap, and it's pretty easy to understand. Even gets into Calculus near the end. Only problem is there's not enough exercises, I think. But other than that, a generally well regarded book. Not important, but I got a kick out of the testimonial on the back:

"It makes alive the contents of the elements of mathematics." - Albert Einstein

Also, when you get to Calculus, James Stewart's "Calculus" is pretty good, and seems to be quite popular. There are much easier books for Calculus, but it's thorough and quite good, in my opinion.

Hope that helps a bit. I'm sure there's differing points of view on what I've said, but it's what I've found to be the best so far, in my limited experience.

P.S. Good thing I save my posts before I submit. Of course, PF would become inaccessible as I write a really long forum post. Glad I didn't lose it after all that typing.

Thanks for the advice and helping out. I actually looked into the matter and found a few sources that help explain how to easily do certain math functions in the head without using paper or a calculator, so i'll definitely work towards that goal as a supplement. Your pyramid analogy is spot on, so in layers I shall proceed on this journey.

I ended up getting both algebra for dummies books, along with their respective workbooks, in a lovely deal too good to pass up. And i'll definitely consult online resources if I find anything too complicated.

You're a LAW student and you can't do word problems? Seriously? They're rarely anything more than logic problems...

I find mathematical word problems different than formal logic, etc. I don't mean to say I can't do them, only that I have trouble with them. Again, probably because I don't have the best grasp of the mathematics needed for completion. Not to mention that throughout my high school education, we rarely practiced word problems. I struggled at first in college Chemistry 1 in dealing with the word problems presented, but that was highly contributed to not having that aforementioned strong foundation. In Chem 2, I was heavily tutored, but prevailed in the end with an A. Those Chemistry classes are literally the last time I've done math in an academic setting, so yeah.