Closing the Gaps: My Journey in Learning Mathematics for Chemical Engineering

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In summary: You're not a 'gifted genius'. You are not unique in your difficulty in learning mathematics. Most people have to struggle at some point. Just be patient and work through the material.
  • #1
Mathnomalous
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Hello! Thanks clicking this thread. Please allow me to trouble you for a few minutes.

I'm about to finish my first semester at CUNY's Bronx Community College. CUNY's math placement test landed me on Math 05, which is basically Algebra 1 remedial class. Even though I'm about to pass that course with an A, I feel I still have huge "gaping holes" in my Math knowledge and I want to correct them before I start taking Calculus. My interests are Physics and Chemistry and my goal is to become a Chemical Engineer.

My Math professor believes I am doing great in Algebra and instead focus on sharpening my Arithmetic; I agree with him but that does not satisfy me. I do not know what order Mathematics starts but I'm assuming it goes Arithmetic → Algebra → Geometry/Trigonometry → Calculus. I want to start from the most basic Arithmetic, so I'm looking for books that assume the reader is mathematically illiterate. I'm looking for training wheels and as I advance then ride on my own.

Now, I'm not a "gifted genius" or anything of the sort; I expect to have huge difficulties. I simply want to have all the Mathematical knowledge I can obtain. If others can learn Mathematics so can I; the only difference between myself and a Math genius is that the dude has been studying longer than me, nothing else; my dreams and goals depend on learning Math, so I have no choice but to learn it. Any assistance you may provide me will be appreciated. Thank you.

edit: http://www.maa.org/devlin/LockhartsLament.pdf [Broken] just read it after checking out more threads related to my problem. I am now utterly confused! Hahah!
 
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  • #2
What kind of arithmetic do you feel you need work on, and what other gaping holes do you think you have in your math knowledge?

The order you've written:
"Arithmetic → Algebra → Geometry/Trigonometry → Calculus"

is more or less the order elementary mathematics is usually taught. And it is true that a lot of mathematics builds on other stuff. But mathematics is not linearly ordered, and there is to some degree some arbitrariness in the order here. For instance, historically, geometry was studied long before most of what we would really consider algebra was developed.
 
  • #3
as an chemical engineer you don't need such an advance math so better focus in your chemistry
 
  • #4
the pro said:
as an chemical engineer you don't need such an advance math so better focus in your chemistry

Calculus isn't an advanced math...it's required for Engineers.

CS
 
  • #5
Mathnomalous said:
Hello! Thanks clicking this thread. Please allow me to trouble you for a few minutes.

I'm about to finish my first semester at CUNY's Bronx Community College. CUNY's math placement test landed me on Math 05, which is basically Algebra 1 remedial class. Even though I'm about to pass that course with an A, I feel I still have huge "gaping holes" in my Math knowledge and I want to correct them before I start taking Calculus. My interests are Physics and Chemistry and my goal is to become a Chemical Engineer.

My Math professor believes I am doing great in Algebra and instead focus on sharpening my Arithmetic; I agree with him but that does not satisfy me. I do not know what order Mathematics starts but I'm assuming it goes Arithmetic → Algebra → Geometry/Trigonometry → Calculus. I want to start from the most basic Arithmetic, so I'm looking for books that assume the reader is mathematically illiterate. I'm looking for training wheels and as I advance then ride on my own.

Now, I'm not a "gifted genius" or anything of the sort; I expect to have huge difficulties. I simply want to have all the Mathematical knowledge I can obtain. If others can learn Mathematics so can I; the only difference between myself and a Math genius is that the dude has been studying longer than me, nothing else; my dreams and goals depend on learning Math, so I have no choice but to learn it. Any assistance you may provide me will be appreciated. Thank you.

edit: http://www.maa.org/devlin/LockhartsLament.pdf [Broken] just read it after checking out more threads related to my problem. I am now utterly confused! Hahah!

You're on the right path...just build your mathematical background by taking the courses you have outlined above. They are designed to give you the necessary tools to prepare you for not only Calculus, but engineering concepts as well.

CS
 
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  • #6
Mathnomalous said:
My Math professor believes I am doing great in Algebra and instead focus on sharpening my Arithmetic;

I'm not sure why. I've really found good arithmetic to be not that useful in geometry and calculus. My arithmetic is totally dreadful, probably since I've never had to use any of it in the last decade or so. If you've mastered algebra, I really don't see how being good at arithmetic is going to be that useful to you.

I expect to have huge difficulties. I simply want to have all the Mathematical knowledge I can obtain.

You have to realize that the arithmetic->algebra->geometry->calculus routine is a tiny, tiny fraction of what mathematics there is. The reason it's taught this way is that calculus is the bare minimal requirement for any sort of science and engineering.

Now if you want to go off the beaten path and look at something really different, there are lots of different areas that you can look at. Wikipedia is pretty good for doing that sort of thing.

the only difference between myself and a Math genius is that the dude has been studying longer than me, nothing else;

I'm not sure that's true. There are people that are really, really good at math, and they tend to pick things up a lot faster than me. One reason that I got my Ph.d. in physics is that I'm not particularly good at math.

Also a lot depends on the quality of teaching. A good math teacher can make the difference between something that is totally obvious and something that is impossible to understand. One problem with thinking that effort will get you somewhere, is that especially with math, sometimes you are expending a huge amount of effort because its being badly taught.
 
  • #7
stewartcs said:
Calculus isn't an advanced math...it's required for Engineers.
And if he plans to stay in the CUNY system, he's got to take 5 classes worth of calculus (calc 1-3, diffEQ, vector calc/linera algebra).

Arithmetic → Algebra → Geometry/Trigonometry → Calculus.
A lot of schools have pre-calc before calc, and it usually covers limits, interest, and some other random odd little things. (It's the first course in the math sequence at most CUNY schools if you don't place into calculus.)

As for starter stuff, if you have no qualms about doing stuff for kids, I adore the BBC maths review sets. home page - look around for the topics you really want to beef up.
 
  • #8
Thanks for the replies. I think I need to explain what my intentions are more clearly so I will list what my goals are:

1) I want and need a solid, robust Mathematics foundation that will allow me to study Physics, Chemistry, and Chemical Engineering properly and efficiently. Mathematics is a tool and I desire to use this tool to express the thoughts and ideas flowing through my head. I want and need to understand what the tool is and how to use it. I want my mathematical knowledge to be "stainless steel-solid" and water-proof. I think Stewartcs addressed this.

2) Building on #1, I desire to understand the mathematical concepts behind this knowledge to satisfy my curiosity. I'd like to understand where concepts come from, what led to them, etc. For example, while (re)learning the quadratic formula, my Math 05 demonstrated how it was derived starting from the general form ax² + bx + c = 0 and ending at -b ± square root b² - 4ac divided by 2a. I was amazed and from that moment I can't stop thinking where other concepts come from and spend considerable amounts of time trying to figure them out. I want to understand why I am doing something and the concept behind that something, not just memorize a series of steps like an automaton.

3) Building from #2 and #3, I am searching for books that assume the reader has little to no previous knowledge of the Mathematics subfield covered but progressively increases the depth of the subject. In other words, I want to start crawling, then have someone hold my hands while I take those first steps, and finally be able to walk on my own to explore the world.

I do not know how Mathematics should be taught. I believed (incorrectly?) that Mathematics began at Arithmetic and progressed from there. I just want to start from 0, 1, 2, 3... basically, I want to build a solid base for my house before I build the walls, roof, piping, etc. Thanks for your patience.
 
  • #9
Mathnomalous -

Arithmetic is some of the first mathematics taught to students because it is simple and useful and necessary for other things they need to be taught, but not because it is in any real sense a foundation or starting point for mathematics.

And, in fact, topics in the foundations of mathematics are out of your reach right now.

You certainly have the right attitude (about wanting to actually understand how things work). Maybe you could be more specific about what it is you want to know?
 
  • #10
mrb said:
And, in fact, topics in the foundations of mathematics are out of your reach right now.
Most of the foundational stuff is taught in the upper-level math courses because it's very dependent on proofs and all sorts of theorems and advanced concepts that you have to learn first.

Building on #1, I desire to understand the mathematical concepts behind this knowledge to satisfy my curiosity. I'd like to understand where concepts come from, what led to them, etc.
Try your textbooks. For example, the Stewart calculus book has digressions into history and sometimes touches on the conceptual stuff.

I just want to start from 0, 1, 2, 3... basically, I want to build a solid base for my house before I build the walls, roof, piping, etc. Thanks for your patience.
Math/history/philosophy books? Maybe "The Nothing that Is: A Natural History of Zero" and working up from there to others in a similar vein?
 
  • #11
mrb said:
Mathnomalous -

Arithmetic is some of the first mathematics taught to students because it is simple and useful and necessary for other things they need to be taught, but not because it is in any real sense a foundation or starting point for mathematics.

And, in fact, topics in the foundations of mathematics are out of your reach right now.

You certainly have the right attitude (about wanting to actually understand how things work). Maybe you could be more specific about what it is you want to know?

Concerning the underlined, I will start from arithmetic because it will likely provide me with what I need to understand more advanced mathematic topics. These 3 books were recommended to me so I will begin with them:

https://www.amazon.com/dp/9708170011/?tag=pfamazon01-20
https://www.amazon.com/dp/9708170011/?tag=pfamazon01-20
https://www.amazon.com/dp/9708170011/?tag=pfamazon01-20

Concerning the bolded, I want to be an efficient and reliable chemical engineer; this means mastering algebra and calculus (and other necessary mathematics) to perform my job to the best of my abilities. I'd like to be able to work on issues like this: http://newsroom.ucla.edu/portal/ucla/ucla-researchers-engineer-bacteria-149726.aspx

Basically, use my knowledge of mathematics, physics, and chemistry to design useful things. For example, I'd like to design a water treatment/power plant hybrid, obtain methane supplies from termites, and/or invent a new and advanced type of electrochemical battery.

Nonetheless, thank you and the rest of you for taking the time to address my concerns.
 
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1. What is "Closing the Gaps: My Journey in Learning Mathematics for Chemical Engineering" about?

"Closing the Gaps: My Journey in Learning Mathematics for Chemical Engineering" is a personal account of a scientist's experience in overcoming challenges and improving their mathematical skills specifically for the field of chemical engineering. It offers insights, tips, and strategies for those who may be struggling with the same obstacles.

2. Who is the intended audience for this book?

This book is primarily targeted towards students or professionals in the field of chemical engineering who may be struggling with mathematics. However, it may also be beneficial for anyone interested in improving their mathematical skills for any scientific or engineering field.

3. What inspired you to write this book?

As a scientist, I have personally experienced the difficulties of learning and applying advanced mathematics in my work. Through my own journey, I have discovered helpful strategies and resources that I wanted to share with others who may be facing similar challenges. I hope to inspire and motivate others to continue learning and growing in their mathematical skills.

4. What can readers expect to gain from reading this book?

Readers can expect to gain a better understanding of how mathematics is used in the field of chemical engineering, as well as practical tips and strategies for improving their own mathematical skills. The book also offers personal anecdotes and insights that readers can relate to and find encouragement from.

5. Are there any recommended prerequisites for reading this book?

While there are no specific prerequisites, a basic understanding of mathematics and chemistry would be beneficial in fully understanding the concepts discussed in the book. However, even readers with limited knowledge in these areas can still benefit from the strategies and tips presented in the book.

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