My Journey With Mathematics

Jomo said:
David Cohen and Michael Sullivan are great math professionals but not gifted in terms of explaining hard concepts for all to grasp.

You can't compare textbooks to study guides as they are not the same. It is like comparing apples and oranges. A study guide, like Pre-Calculus for Dummies, just work out problems while a textbook is quite different from that.

Also there is no book that can explain hard concepts for all to grasp!
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In that case, what should I do? Continue with the textbooks or purchase the study guides?
 
Jomo said:
Study guides are fine!
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Ok. Cool. I need to understand what is going on. The MATH FOR DUMMIES and also the Michael Kelly books are all an easy read. When back on my feet, I plan to replace textbooks with study guides. This will lead to less questions posted here.
 
I'm presently working my way through a math course that I did over 10 years ago, which now is purely interest only. I've no intentions of ever trying to make anything from the course like looking for work etc as I'm past my sell by date for that line of reasoning anymore. I have a great collection of math books from many specialist areas of expertise, some I understand very well but find some of the basic skills I did not acquire at school trip me up regularly. I've always maintained that a person cannot be given "understanding", you either gain that through much study practice or for some reason the "penny" just seems to drop in place! In saying that I've noticed over the years that some mathematicians are very good at solving problems and number crunching, but have also seen that understanding in some areas of the subject are very much lacking. The four books I'm working my way through now are study guides and are very good, designed to give the student guidance and test your ability to reason and work out solutions to problems. When I've finished this book 2 it's then probably is a good time to recap over books 1 and 2 again before I move onto books three and four, which seem to become much more involved. When I was at school and a math lesson came along I dreaded it, the teacher writing things on the board like a^3 x a^3 x a^3 = and we were left to work it out, clearly to me that example had no prior explanation to show that a^3 x a^3 x a^3 came from a x a x a x a x a x a x a x a. and could then be written as "a^9". Clearly some of us had absolutely not idea what it meant, and no effort was put in to explain it as I can remember. The student just gets left behind at that point, and back then in the 1970's books were not freely available as they are now, and no such thing as Google.

In college ideas seemed to change, the tutors then writing things down and explaining the subject more clearly. I'd also learned over my lifetime that some math tutors did not want to pass on the explanations of the subject as they thought when you understand math you are clearly a cut above the human race?

Math books are very good but they are in most cases just that, a book written and presented by an author who is a specialist in some areas of expertise, and the student reading that book is not necessarily going to get the insight required from a learner point of view. I've found that study guides like the ones I have seem to be well written and provide examples to built understanding before the student is presented with activities to complete. I'd probably to correct to say for the learner that study guides are the way to go and for the student refreshing knowledge in given subjects, then math books are the way to refresh previously understood training when required.
 
Probability said:
I'm presently working my way through a math course that I did over 10 years ago, which now is purely interest only. I've no intentions of ever trying to make anything from the course like looking for work etc as I'm past my sell by date for that line of reasoning anymore. I have a great collection of math books from many specialist areas of expertise, some I understand very well but find some of the basic skills I did not acquire at school trip me up regularly. I've always maintained that a person cannot be given "understanding", you either gain that through much study practice or for some reason the "penny" just seems to drop in place! In saying that I've noticed over the years that some mathematicians are very good at solving problems and number crunching, but have also seen that understanding in some areas of the subject are very much lacking. The four books I'm working my way through now are study guides and are very good, designed to give the student guidance and test your ability to reason and work out solutions to problems. When I've finished this book 2 it's then probably is a good time to recap over books 1 and 2 again before I move onto books three and four, which seem to become much more involved. When I was at school and a math lesson came along I dreaded it, the teacher writing things on the board like a^3 x a^3 x a^3 = and we were left to work it out, clearly to me that example had no prior explanation to show that a^3 x a^3 x a^3 came from a x a x a x a x a x a x a x a. and could then be written as "a^9". Clearly some of us had absolutely not idea what it meant, and no effort was put in to explain it as I can remember. The student just gets left behind at that point, and back then in the 1970's books were not freely available as they are now, and no such thing as Google.

In college ideas seemed to change, the tutors then writing things down and explaining the subject more clearly. I'd also learned over my lifetime that some math tutors did not want to pass on the explanations of the subject as they thought when you understand math you are clearly a cut above the human race?

Math books are very good but they are in most cases just that, a book written and presented by an author who is a specialist in some areas of expertise, and the student reading that book is not necessarily going to get the insight required from a learner point of view. I've found that study guides like the ones I have seem to be well written and provide examples to built understanding before the student is presented with activities to complete. I'd probably to correct to say for the learner that study guides are the way to go and for the student refreshing knowledge in given subjects, then math books are the way to refresh previously understood training when required.
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1. What is the name of the books (all four parts) in your library that you are currently studying?

2. What do you think about the MATH FOR DUMMIES series?

3. I think you should check out Professor Leonard on You Tube. He is probably the best math professor on the internet.

4. Math textbook, in particular, are like hieroglyphics to most students. What do you say? Which do you prefer for self-study and review?
 
I downloaded a Michael Sullivan Precalculus textbook. This is the book I will use for the remainder of my Precalculus self-study.

The downloaded pages allow me to copy and paste material. The rest of the journey should be a lot easier. The Sullivan textbook is so much better for what I want to know about the subject. I will not trash or give away my David Cohen textbook but instead use it as reference and practice from time to time.
 
My goal in terms of mathematics is divided into three sections:

1. Learn Calculus 1-3 to a very comfortable level.

2. Master word problems in terms of high school algebra.

3. Develop a solid understanding of basic probability.

How can this be accomplished? I am seeking serious replies. If you plan to belittle or put me down with your reply, rethink it. You say?
 
harpazo said:
My goal in terms of mathematics is divided into three sections:

1. Learn Calculus 1-3 to a very comfortable level.

2. Master word problems in terms of high school algebra.

3. Develop a solid understanding of basic probability.

How can this be accomplished? I am seeking serious replies. If you plan to belittle or put me down with your reply, rethink it. You say?
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I would start with 2, then move to 3 and then 1. Algebra is essential to 1 and 3.

-Dan
 
Probability said:
I'm presently working my way through a math course that I did over 10 years ago, which now is purely interest only.

SAME SITUATION FOR ME BUT I GET CRITICIZED BY FRIENDS AND FAMILY WHO DO NOT SEE THE PRACTICALITY OF MATH REVIEW, ESPECIALLY AT MY AGE.

I've no intentions of ever trying to make anything from the course like looking for work etc as I'm past my sell by date for that line of reasoning anymore.

SAME HERE. I HAVE NO INTENTION TO FIND WORK AS A TEACHER. ALTHOUGH TUTORING MAY STILL BE POSSIBLE AT 55. WHAT DO YOU THINK?

I have a great collection of math books from many specialist areas of expertise, some I understand very well but find some of the basic skills I did not acquire at school trip me up regularly.

YOU HIT THE NAIL ON THE HEAD. I GREW UP IN NYC. I WENT TO NYC PUBLIC SCHOOLS. PLACED IN REMEDIAL CLASSES EARLY ON IN MY EDUCATION. I DID NOT LEARN MOST OF THE MAIN TOPICS NEEDED TO SUCCEED IN CALCULUS. REMEDIAL MATH IS BASICALLY THAT---REMEDIAL OR BABY STUFF.

I've always maintained that a person cannot be given "understanding", you either gain that through much study practice or for some reason the "penny" just seems to drop in place! In saying that I've noticed over the years that some mathematicians are very good at solving problems and number crunching, but have also seen that understanding in some areas of the subject are very much lacking.

INTELLIGENCE IS A GIFT. SOME PEOPLE ARE BORN WITH THIS TALENT AND OTHERS ARE NOT ACADEMICALLY GIFTED. SOME PEOPLE ARE EXCELLENT MATHEMATICIANS BUT CANNOT PAINT A ROOM OR HANG A PICTURE ON THE WALL. SOME ARE HANDY; SOME NEED A HANDY PERSON TO HANG UP A CURTAIN. VERY FEW CAN DO BOTH.

The four books I'm working my way through now are study guides and are very good, designed to give the student guidance and test your ability to reason and work out solutions to problems. When I've finished this book 2 it's then probably is a good time to recap over books 1 and 2 again before I move onto books three and four, which seem to become much more involved.

WHAT BOOKS ARE YOU TALKING ABOUT? PLEASE SHARE THE TITLES AND AUTHORS OF THE BOOKS.

When I was at school and a math lesson came along I dreaded it, the teacher writing things on the board like a^3 x a^3 x a^3 = and we were left to work it out, clearly to me that example had no prior explanation to show that a^3 x a^3 x a^3 came from a x a x a x a x a x a x a x a. and could then be written as "a^9".

THE MATH FOR DUMMIES SERIES DOES EXACTLY THAT---BREAKS DOWN THE PROBLEM. IT IS IN PREALGEBRA THAT EXPRESSIONS ARE BROKEN DOWN AS YOU SHOWED. IN A PREALGEBRA TEXTBOOK, A^2 IS BROKEN DOWN TO THIS:
A^1 • A^1 = A^(1 + 1) = A^2. IF YOU SKIP COURSES, PROBLEMS ARISE. THIS WAS MY SITUATION.

I WENT INTO INTERMEDIATE ALGEBRA/TRIG BECAUSE I GUESSED CORRECTLY WHEN TAKING THE CUNY ENTRANCE TEST. BASED ON MY SCORE, THE MATH DEPARTMENT DECIDED TO PLACE ME IN ALGEBRA 2 AND TRIGONOMETRY BEFORE I HAD TAKEN ALGEBRA 1. IT WAS ALL BASED ON A STANDARDIZED TEST SCORE. THE FACT IS THAT I WAS NOT READY FOR ALGEBRA 2 AND TRIGONOMETRY. YOU SEE, I NEVER TOOK GEOMETRY OR TRIG IN HIGH SCHOOL AS IT IS NOT REQUIRED FOR REMEDIAL STUDENTS.

Clearly some of us had absolutely not idea what it meant, and no effort was put in to explain it as I can remember. The student just gets left behind at that point, and back then in the 1970's books were not freely available as they are now, and no such thing as Google.

I GOT LEFT BEHIND NUMEROUS TIMES IN NYC PUBLIC SCHOOLS. SOCIAL PROMOTION IS THE ONLY REASON WHY I GRADUATED FROM HIGH SCHOOL. YOU KNOW WHAT SOCIAL PROMOTION IS, RIGHT? PASSING STUDENTS TO MAKE ROOM FOR THOSE COMING BEHIND. IN ALL HONESTY, I SHOULD NOT HAVE A HIGH SCHOOL DIPLOMA. I ALSO GRADUATED FROM TWO CUNY COLLEGES. TALK ABOUT A MIRACLE!! HOW DOES A PERSON LIKE ME GRADUATE FROM NOT ONE BUT TWO CUNY COLLEGES? EXPLAIN THAT.... NO PUN INTENDED.

In college ideas seemed to change, the tutors then writing things down and explaining the subject more clearly. I'd also learned over my lifetime that some math tutors did not want to pass on the explanations of the subject as they thought when you understand math you are clearly a cut above the human race?

WHAT DO YOU MEAN HERE?

Math books are very good but they are in most cases just that, a book written and presented by an author who is a specialist in some areas of expertise, and the student reading that book is not necessarily going to get the insight required from a learner point of view.

I HAVE BEEN SAYING THIS FOR YEARS.

I've found that study guides like the ones I have seem to be well written and provide examples to built understanding before the student is presented with activities to complete. I'd probably to correct to say for the learner that study guides are the way to go and for the student refreshing knowledge in given subjects, then math books are the way to refresh previously understood training when required.

I WILL NEED TO LOOK UP STUDY GUIDES. TO BE HONEST, I ASK MYSELF WHY I CONTINUE TO ENJOY MATH AND HAVE A PASSION FOR NUMBERS AT 55. I AM WAY BEYOND THE SCHOOL YEARS BUT FIND MYSELF ALWAYS YEARNING NOT TO FORGET THE LITTLE BIT OF MATH I HAVE BEEN INTRODUCED TO HERE AND IN OTHER SITES. I HAVE A LONG WAY TO GO BUT MY GOAL IS TO REACH CALCULUS 1 AND MAKE IT THROUGH 2 AND FINALLY 3. I ALSO LIKE PROBABILITY AND SERIOUSLY NEED HELP.
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I define myself to be an odd ball. WHY DO I LIKE MATH AT 55 YEARS OLD? What is wrong with me? I am never going to be a teacher. I may never get a tutoring job. I find this stuff fascinating and even exciting. Yes, I get excited when I see an equation. Don't you wish your students were like me?
 
I was watching the TV the other evening when the news was on, covid-19 was being discussed and family members were being asked about schooling their kids. There are many different view points on this subject, but one lady said that teaching kids their times tables among other math's was not absolutely necessary. I can't remember the specifics of her conversation and reasoning why. I've found in my life time that education has become very complex and even after studying a subject all your life, you might not fully understand it. The problem I always found with school education was that the teachers at that time were more like instructors, they gave you a problem and that was it, and if they presented an example, it was not broken down enough for people like me to understand how the building blocks of it had been assembled. They always had this bad attitude as I saw it, saying things like, "you must get the understanding from a mysterious source". Later years I understood that some teachers were indeed "step in's" for the other teachers and actually the teachers themselves were almost clueless in the understanding of the subject as well. You could recognise this when the teacher was parrot fashion copying word for word examples from other written material. I experienced this a lot at university in my later years.

In the time of the end that we are in, you don't need to be the best mathematician, nor the best electrician, nor the best engineer, but the best scientist and find a damn cure for diseases like covid-19 and cancer. If you gained a Phd in anything what good would it be if there were nobody to share the talent with!
 
Probability said:
I was watching the TV the other evening when the news was on, covid-19 was being discussed and family members were being asked about schooling their kids. There are many different view points on this subject, but one lady said that teaching kids their times tables among other math's was not absolutely necessary. I can't remember the specifics of her conversation and reasoning why. I've found in my life time that education has become very complex and even after studying a subject all your life, you might not fully understand it. The problem I always found with school education was that the teachers at that time were more like instructors, they gave you a problem and that was it, and if they presented an example, it was not broken down enough for people like me to understand how the building blocks of it had been assembled. They always had this bad attitude as I saw it, saying things like, "you must get the understanding from a mysterious source". Later years I understood that some teachers were indeed "step in's" for the other teachers and actually the teachers themselves were almost clueless in the understanding of the subject as well. You could recognise this when the teacher was parrot fashion copying word for word examples from other written material. I experienced this a lot at university in my later years.

In the time of the end that we are in, you don't need to be the best mathematician, nor the best electrician, nor the best engineer, but the best scientist and find a damn cure for diseases like covid-19 and cancer. If you gained a Phd in anything what good would it be if there were nobody to share the talent with!
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There are several reasons that make clear just how terrible the educational system has become in the United States.

1. Teaching to the test. No actual learning.

2. Social promotion to satisfy parents who are kept in the dark about what is actually going on in the schools.

3. Lowering test standards to satisfy complaining parents.

4. Hiring OUT OF SUBJECT teachers.

5. Hiring subs with no teacher training and/or classroom experience.

What do you say about 1-5 as listed here?
 
harpazo said:
There are several reasons that make clear just how terrible the educational system has become in the United States.
1. Teaching to the test. No actual learning.
2. Social promotion to satisfy parents who are kept in the dark about what is actually going on in the schools.
3. Lowering test standards to satisfy complaining parents.
4. Hiring OUT OF SUBJECT teachers.
5. Hiring subs with no teacher training and/or classroom experience.
What do you say about 1-5 as listed here?
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I basically agree with all of those. But I really doubt that you would agree with any of my solutions.
First I say that teacher unions must be striped of any ability to comment in salaries. Mathematics teachers should earn more than others. But that should come with conditions. In my state the requirement to be qualified as a secondary (grades 9 thru 12) mathematics teacher one must have the equivalent of a mathematics major. That deserves more pay. But teacher union raise **** about that. I have no objection if there were similar requirements for science and econometrics teachers.
 
pka said:
I basically agree with all of those. But I really doubt that you would agree with any of my solutions.
First I say that teacher unions must be striped of any ability to comment in salaries. Mathematics teachers should earn more than others. But that should come with conditions. In my state the requirement to be qualified as a secondary (grades 9 thru 12) mathematics teacher one must have the equivalent of a mathematics major. That deserves more pay. But teacher union raise **** about that. I have no objection if there were similar requirements for science and econometrics teachers.
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I concur. I also go further to say that any discipline requiring calculus 1-3 and beyond should lead to more pay. Personally, I despise unions. I belong to a union now that brags about how good they are but have nothing to say when employees go to the dentist office, for example, and are told by the receptionist that payment must be made prior to seeing the dentist because the union is not making payments.

So, what good is the union? What good is it to be a member of the union? The union takes money from my biweekly check but they do nothing in terms of fighting for employees when help is needed. In fact, pka, it was the union who decided which employees to keep at the job during the pandemic and which to place on furlough WITHOUT PAY.

I am one of 56 employees placed on furlough without pay. Mathematics is a very challenging discipline. So is physics, chemistry, economics, accounting, etc. I agree that people majoring in anything related to science (math and physics, for example), should be paid a lot more money. A high school math teacher should make more than someone teaching fractions in grade 5. A calculus teacher should make more than someone teaching middle school and so on.
 
harpazo said:
There are several reasons that make clear just how terrible the educational system has become in the United States.

1. Teaching to the test. No actual learning.

2. Social promotion to satisfy parents who are kept in the dark about what is actually going on in the schools.

3. Lowering test standards to satisfy complaining parents.

4. Hiring OUT OF SUBJECT teachers.

5. Hiring subs with no teacher training and/or classroom experience.

What do you say about 1-5 as listed here?
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Totally agree
 
pka said:
I basically agree with all of those. But I really doubt that you would agree with any of my solutions.
First I say that teacher unions must be striped of any ability to comment in salaries. Mathematics teachers should earn more than others. But that should come with conditions. In my state the requirement to be qualified as a secondary (grades 9 thru 12) mathematics teacher one must have the equivalent of a mathematics major. That deserves more pay. But teacher union raise **** about that. I have no objection if there were similar requirements for science and econometrics teachers.
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I don't know about that one to be honest. I'd ask the question why?

I'll provide you with a real world case to show my reasoning why a mathematician should not be regarded as superior to other experts in their chosen areas of expertise.

It's a bit long...

A lady driver was driving her car along the highway when she approached a bend and continued to drive around this bend normally when she ran straight into the rear of a parked HGV. She complained to the insurance company and police about the way this HGV was parked on the side of the highway on a blind bend. They went to court and the HGV driver got a Phd in mathematics to write him a defense about his parked HGV and because the mathematician was a Phd the Judge accepted his report and the lady driver lost the case.

She was not happy and looked to find help. She came across experts in collision investigations (forensics). They heard her case and agreed to go and inspect the accident site. They took measurements and photos of the site where the accident occurred and said that they had sufficient evidence to appeal the case. Upon appealing the case the Phd was asked in court where he got his evidence from to compile his report on behalf of the HGV driver, the Phd said he had used college physics. The judge barred the Phd from ever giving evidence in court again with regards to collision investigations. The lady was cleared of all blame for the accident.

What is a person worth I don't know is the answer. What I do know however is that text book math's is only the fundamental basics of the subject,and when applied into industries to use as experts, the subject changes dramatically.
 
Probability said:
I don't know about that one to be honest. I'd ask the question why?

I'll provide you with a real world case to show my reasoning why a mathematician should not be regarded as superior to other experts in their chosen areas of expertise.

It's a bit long...

A lady driver was driving her car along the highway when she approached a bend and continued to drive around this bend normally when she ran straight into the rear of a parked HGV. She complained to the insurance company and police about the way this HGV was parked on the side of the highway on a blind bend. They went to court and the HGV driver got a Phd in mathematics to write him a defense about his parked HGV and because the mathematician was a Phd the Judge accepted his report and the lady driver lost the case.

She was not happy and looked to find help. She came across experts in collision investigations (forensics). They heard her case and agreed to go and inspect the accident site. They took measurements and photos of the site where the accident occurred and said that they had sufficient evidence to appeal the case. Upon appealing the case the Phd was asked in court where he got his evidence from to compile his report on behalf of the HGV driver, the Phd said he had used college physics. The judge barred the Phd from ever giving evidence in court again with regards to collision investigations. The lady was cleared of all blame for the accident.

What is a person worth I don't know is the answer. What I do know however is that text book math's is only the fundamental basics of the subject,and when applied into industries to use as experts, the subject changes dramatically.
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Now, let's get back to solving math problems.
 
harpazo said:
I have "playing" with math textbooks for years. I came to the following realization (because it cannot be any other way).

1. I cannot retain information for too long. I review, say, chapters 1 and 2 in any given textbook but by the time I get to chapter 3, chapters 1 and 2 slowly begin to disappear from memory.

2. No matter how many questions I answer or how much time I dedicate to review material learned long ago, I will NEVER be like MarkFL or pka or Dr. Peterson and the rest of the truly gifted mathematicians here and in other forums.

3. Posting too many questions in one day leads to more confusion and frustration. How many questions should be posted per week? One? Two? Three? How about one per day?

4. Math is a hobby for me. However, I often forget that mathematics is not going to land me a great teaching career or a scientist job at NASA, or a bridge engineer position, etc.

5. This math site and others like it has taught me humility. Before joining online math groups and sites, I actually convinced myself that mathematics was truly a God given talent and/or skill when in actuality I know less than the worst student in a public school setting.

What do you say?
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Perseverance and love for the subject are an important key to success. Besides, the many tools we have today, like this forum and similar online tools will most of the time help you.
 
yoscar04 said:
Perseverance and love for the subject are an important key to success. Besides, the many tools we have today, like this forum and similar online tools will most of the time help you.
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A few things about me.

1. My days to "MAKE IT" in life are over.

2. I am 55 years old.

3. I am not learning advanced math to become a teacher. If I can somehow land a tutor job, and make extra money, terrific! If not, who cares, right?

4. Mathematics is a hobby and nothing more.

5. I put all other hobbies aside to do math, including Bible study time. This is not a good idea.

6. I had to give up playing guitar to avoid trouble with roommates. You see, I don't have my own place. Rent is out of control in NYC.

7. Currently on furlough WITHOUT PAY due to COVID-19. I hope to be back to work in the Fall.
 
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