Best scientific measurement books according to redditors

First, you might want to start with /r/matheducation. They’re actually experts in this subject.

You can read work by hundreds of experts in child psychology/development, pedagogy, the philosophy of mathematics, the intuitive/psychological foundations of mathematics, etc. Personally I’m a fan of Piaget, Bruner, Papert, and like-minded thinkers, who advocate a child-centered “constructivist” approach to education. But there are certainly respectable educators and researchers who favor a more structured and top-down approach.

If you want to read concretely about the differences between typical US instruction and Chinese instruction in the 1990s, read Liping Ma’s book Knowing and Teaching Elementary Mathematics

Or watch this video from a few years ago discussing the TIMSS study and criticizing Khan Academy.

Or to see what a particular group of young children could learn with some expert guidance, check out Zvonkin’s book.

You might have read Lockhart’s Lament. He provides an alternative way of teaching high school mathematics in his book Measurement.

I like this concise theory of mathematical learning. YMMV. Here’s a short essay by Minksy about why mathematics is hard to learn.

If you want lesson plans and curriculum guidance, look to the American NCTM, who have been making detailed materials available for decades. Also look up math circles (both online materials and physical groups meeting in your area).

You might like this book by Van de Walle about general elementary teaching, or this book by Lenchner about problem solving.

Many people seem to like the Singapore math books. Read about Singapore’s curriculum.

If you ask homeschooling parents in your area, you can probably find strong opinions about curricula. Just searching around the web, many keywords about elementary math books etc. seem to lead to homeschooling sites. (This makes some sense: they have some free time, like to write about their experiences and form online communities, and do more personal evaluation of curricula than schoolteachers can necessarily have time/political power to do.)

There are hundreds of available books of mathematical puzzles and games, dozens of different types of physical manipulatives, and thousands of books, papers, essays, etc. about how to organize, order, and teach students of every imaginable age and background

If you have a particular age group / level of prior preparation / desired set of topics in mind, there might be some more specific materials people can point to. Are we talking about 4-year-olds? 10-year-olds? High school olympiad preparation? Are you interested in basic arithmetic? Geometry? Algebra? Do you have 1 advanced student to teach? 50 students of varying skill levels?

"Probability theory is just a branch of measure theory" is something analysts say to annoy probabilists. It has just enough truth to be annoying but not enough to truly sting. After all the first third of the typical graduate level probability text, such as Chung or Billingsley is mostly measure theory. But then probability theory goes off in its own direction with some of the deepest theorems in mathematics, which have no analogs in any other part of mathematics.

No, you really shouldn't.

Open textbooks are a better route to go than paying hundreds of dollars (especially for high school/early college material). The Stitz-Zeager College Algebra text is a good book.

Also, Paul Lockhart's Measurement is also a good place to start.

For undergrad probability, Pitman's book or Ross's two books here and here.

For graduate probability, Billingsley (h/t /u/DCI_John_Luther), Williams or Durrett.

I highly recommend you these books: labmaths and at the bench

1. Ross - First Course in Probability (Calculus based probability, undergraduate level, good introduction to probability)
   
   http://www.amazon.com/First-Course-Probability-9th-Edition/dp/032179477X
   
   
2. Rice - Mathematical Statistics (introduction to statistics, focuses on applications with data, great book, includes good probability review)
   
   http://www.amazon.com/Mathematical-Statistics-Analysis-Available-Enhanced/dp/0534399428
   
   
3. Billingsley - Probability and Measure (graduate, measure-theoretic probability)
   
   http://www.amazon.com/Probability-Measure-Patrick-Billingsley/dp/1118122372
   
   
4. Bickel & Doksum - Mathematical Statistics (graduate level statistical theory, much more theoretical than Rice, can be a difficult book to learn from but it is a great reference)
   
   http://www.amazon.com/Mathematical-Statistics-Selected-Topics-Edition/dp/0132306379
   
   EDIT:
   
   Most likely Rice will be the best book for a comprehensive look at prob/stat, and it is sufficiently technical.
   

This is incredibly on-topic:

Remember Paul Lockhart of “Lockhart’s Lament” fame? (If not: Let’s just say: IMHO, he hits the nail that is your problem right on its head.)

Well, I mailed him back then, and he promised us a book, to teach one how to think like a mathematician. A “textbook” to finally get rid of that nightmare that you, me, and so many others described, and learn math the right way.

Well, last week he e-mailed me (and many others), that his book is done!

http://www.amazon.com/Measurement-Paul-Lockhart/dp/0674057554/

Here’s the original e-mail:

> Dear Readers of A Mathematician's Lament,

> I wanted to let you know that I have a new book out called Measurement. This is my attempt to explain and illustrate, in an honest and heartfelt way, what it is that mathematicians do and why we do it. On one level, you could say that the book is about geometry and analysis, viewed from a modern mathematical perspective, along with natural and (I hope) engaging problems to work on. But really it's a book about me and the way I think, and what it is that I find so beautiful and compelling about math. I would hate for anyone to call it a textbook (it's way too fun), yet, if you want to really understand the mathematics of measurement in a deep and intuitive, intellectually serious way, then this is the book I would recommend. That's why I wrote it: to see if I could. I'm sure there are ways in which I have failed in the book to get across what I wanted to say, but overall I think I did a pretty good job conveying how I think and feel about mathematics, in what I hope is a refreshing new way---just really being me, and speaking to you person to person. Anyway, the book is out, and I would be very curious to know what you think of it.

> Yours,

> Paul

P.S.: As far as I can tell, he prefers not to be contacted too much, but to be left alone. I want to respect that. So please don’t do as I did. :)

P.P.S.: Don’t get angry at other mathematicians/engineers, who learned math in the color-by-the-number style. They are also just innocent victims. It’s not their intention to annoy or harm you. Maybe suggesting this book to them can make their lives nicer too. ;)

https://www.amazon.com/Lab-Math-Measurements-Calculations-Quantitative/dp/0879696346

Last time I ordered something that came in below the 35$ limit, I preordered a math textbook!

It should show up on my last day of classes! I can't wait!

Hell yeah!

Like, my brain and special interests all lean towards the Liberal Arts and Humanities.

But math, logic, and programming calm me the hell down.

Do you have any idea how stressful it is that people can't agree on historical interpretations? Or how to best lead a group of people?

Math has answers and makes sense. I'm with Plato. It is this pure and glorious thing. It's why I love Jesus being described as "ὁ λόγος" (which relates to logic and all the rest). To be clear, you don't need to believe Jesus is the logos to appreciate how kickass math is. Plato sure didn't :P

Also, OP! This book by a Mathematician has a really cool take on teaching and learning and understanding math. Since you do it for fun, definitely would be worth checking out.

If you can't afford it, PM me and I'll send you my copy when my wife is done reading it :)

Further reading/research: (Not all of which I've gotten to read yet. Some of which may be quite tangentially relevant to the discussion at hand along with the books and sites I mentioned above. Consider this more a list of books pertaining to the history of technology, machining, metrology, some general science and good engineering texts.)

Dan Gelbart's Youtube Channel

Engineerguy's Youtube Channel

Nick Mueller's Youtube Channel

mrpete222/tubalcain's youtube channel

Tom Lipton (oxtools) Youtube Channel

Suburban Tool's Youtube Channel

NYCNC's Youtube Channel

Computer History Museum's Youtube Channel

History of Machine Tools, 1700-1910 by Steeds

Studies in the History of Machine Tools by Woodbury

A History of Machine Tools by Bradley

Tools for the Job: A History of Machine Tools to 1950 by The Science Museum

A History of Engineering Metrology by Hume

Tools and Machines by Barnard

The Testing of Machine Tools by Burley

Modern machine shop tools, their construction, operation and manipulation, including both hand and machine tools: a book of practical instruction by Humphrey & Dervoort

Machine-Shop Tools and Methods by Leonard

A Measure of All Things: The Story of Man and Measurement by Whitelaw

Handbook of Optical Metrology: Principles and Applications by Yoshizawa

Angle of Attack: Harrison Storms and the Race to the Moon by Gray

Machine Shop Training Course Vol 1 & 2 by Jones

A Century of Electrical Engineering and Computer Science at MIT, 1882-1982

Numerical Control: Making a New Technology by Reintjes

History of Strength of Materials by Timoshenko

Rust: The Longest War by Waldman

The Companion Reference Book on Dial and Test Indicators: Based on our popular website www.longislandindicator.com by Meyer

Optical Shop Testing by Malacara

Lost Moon: The Preilous Voyage of Apollo 13 by Lovell and Kruger

Kelly: More Than My Share of It All by Johnson & Smith

Skunk Works: A Personal Memoir of My Years at Lockheed by Rich & Janos

Unwritten Laws of Engineering by King

Advanced Machine Work by Smith

Accurate Tool Work by Goodrich

Optical Tooling, for Precise Manufacture and Alignment by Kissam

The Martian: A Novel by Weir

Roark's Formulas for Stress and Strain by Young Budynas & Sadegh

Materials Selection in Mechanical Design by Ashby

Slide Rule: The Autobiography of an Engineer by Shute

Cosmos by Sagan

Nuts, Bolts, Fasteners and Plumbing Handbook by Smith Carol Smith wrote a number of other great books such as Engineer to Win.

Tool & Cutter Sharpening by Hall

Handbook of Machine Tool Analysis by Marinescu, Ispas & Boboc

The Intel Trinity by Malone

Manufacturing Processes for Design Professionals by Thompson

A Handbook on Tool Room Grinding

Tolerance Design: A Handbook for Developing Optimal Specifications by Creveling

Inspection and Gaging by Kennedy

Precision Engineering by Evans

Procedures in Experimental Physics by Strong

Dick's Encyclopedia of Practical Receipts and Processes or How They Did it in the 1870's by Dick

Flextures: Elements of Elastic Mechanisms by Smith

Precision Engineering by Venkatesh & Izman

Metal Cutting Theory and Practice by Stephenson & Agapiou

American Lathe Builders, 1810-1910 by Cope As mentioned in the above post, Kennth Cope did a series of books on early machine tool builders. This is one of them.

Shop Theory by Henry Ford Trade Shop

Learning the lost Art of Hand Scraping: From Eight Classic Machine Shop Textbooks A small collection of articles combined in one small book. Lindsay Publications was a smallish company that would collect, reprint or combine public domain source material related to machining and sell them at reasonable prices. They retired a few years ago and sold what rights and materials they had to another company.

How Round Is Your Circle?: Where Engineering and Mathematics Meet by Bryant & Sangwin

Machining & CNC Technology by Fitzpatrick

CNC Programming Handbook by Smid

Machine Shop Practice Vol 1 & 2 by Moltrecht

The Elements of Computing Systems: Building a Modern Computer from First Principles A fantastic book with tons of free online material, labs, and courses built around it. This book could take a 6th grader interested in learning, and teach them the fundamentals from scratch to design a basic computer processor and programming a simple OS etc.

Bosch Automotive Handbook by Bosch

Trajectory Planning for Automatic Machines and Robots by Biagiotti & Melchiorri

The Finite Element Method: Its Basis and Fundamentals by Zhu, Zienkiewicz and Taylor

Practical Treatise on Milling and Milling Machines by Brown & Sharpe

Grinding Technology by Krar & Oswold

Principles of Precision Engineering by Nakazawa & Takeguchi

Foundations of Ultra-Precision Mechanism Design by Smith

I.C.S. Reference Library, Volume 50: Working Chilled Iron, Planer Work, Shaper and Slotter Work, Drilling and Boring, Milling-Machine Work, Gear Calculations, Gear Cutting

I. C. S. Reference Library, Volume 51: Grinding, Bench, Vise, and Floor Work, Erecting, Shop Hints, Toolmaking, Gauges and Gauge Making, Dies and Die Making, Jigs and Jig Making
and many more ICS books on various engineering, technical and non-technical topics.

American Machinists' Handbook and Dictionary of Shop Terms: A Reference Book of Machine-Shop and Drawing-Room Data, Methods and Definitions, Seventh Edition by Colvin & Stanley

Modern Metal Cutting: A Practical Handbook by Sandvik

Mechanical Behavior of Materials by Dowling

Engineering Design by Dieter and Schmidt

[Creative Design of Products and Systems by Saeed]()

English and American Tool Builders by Roe

Machine Design by Norton

Control Systems by Nise

That doesn't include some random books I've found when traveling and visiting used book stores. :)

If you want to see where he went as a means to continue his ideas, try his next book, Measurement.

Firstly I think you are right about measurement involving constraint. Secondly I'd like to say that constraint isn't necessarily a bad thing. I could reframe the word constraint as focus and it might be seen as more positive.

I read a book on the history of metrology a while back, I think its was this one;

https://www.amazon.com/World-Balance-Historic-Absolute-Measurement/dp/0393343545

and I remember being struck how what I thought was a purely technical effort very quickly turned out to have deep philosophical implications. The point was made (and this is from memory so don't quote me) how the physicists thought of themselves as studying the basic nature of reality while the metrologists were seen as mere technicians doing the grunt work of determining the scales the physicists would measure with. However in creating these scales it seems the metrologists had as much claim if not more so than the physicists had of really touching the basic nature of reality.

All this has brought to mind another notion I think is relevant to this discussion and that is to begin to measure something you must first invent the scale.

Try to find entry points that interest you personally, and from there the next steps will be natural. Most books that get into the nitty-gritty assume you're in school for it and not directly motivated, at least up to early university level, so this is harder than it should be. But a few suggestions aimed at the self-motivated: Lockhart Measurement, Gelfand Algebra, 3blue1brown's videos, Calculus Made Easy, Courant & Robbins What Is Mathematics?. (I guess the last one's a bit tougher to get into.)

For physics, Thinking Physics seems great, based on the first quarter or so (as far as I've read).

I think this book is super handy to have around:
https://www.amazon.com/Lab-Math-Measurements-Calculations-Quantitative/dp/0879696346

It covers the math for all sorts of lab techniques and has one of the best versions of the dilution formula I've found;

[(Concentration you want) / (Concentration you have)] * Total reaction volume = volume of stock to add to reaction.

Awesome! As mentioned, Rudin, Folland, and Royden are the gold standards of measure theory, at least from what I have heard from professors and the internet. I'm sure other people have found other good ones! Another few I somewhat enjoy are Capinski and Kopp and Dudley, as those are more based on developing probability theory. Two of my professors also suggested Billingsley, though I have not really had a good chance to look at it yet. They suggested that one to me after I specifically told them I want to learn measure theory for its own right as well as onto developing probability theory. What is your background in terms of analysis/topology? Also, I am teaching myself basic measure theory (measures, integration, L^p spaces), then I think that should be enough to look into advanced probability. Feel free to PM me if you need some help finding some of these books! I prefer approaching this from the pure math side, so mathematical statistics gets a bit too dense for me, but either way, I would look at probability then try to apply it to statistics, especially at a graduate level. But who am I to be doling out advice?!

*Edit: supplied a bit more context.

I honestly thought I was in /r/Showerthoughts for a moment.

> Geometry class is pointless

On topic. I really think you should read Measurement by Paul Lockhart Maybe it will reframe what a proof is and why this is valuable.

Get her the Foundations of Measurement Volumes I-III.

Measures of Genius by Alan Durden is a book about the scientists whose names are used for SI units, such as the volt (Alessandro Volta) and the watt (James Watt).

The book is available from Amazon and a news article about it is here.

I work in Food Safety / QC. My chemistry and math grades were mediocre.

The extent of chemistry I’m expected to understand involves knowing reactions on biological media & reagents, easily referenced materials. The complex chemistry is handled by Chemists.

Math consists of basic lab calculations (serial dilutions, microbial counts, molarity, etc.). Statistics is helpful if you want to understand sampling plans, but isn’t necessary for bench work.

If you’re concerned, Lab Math provides a comprehensive overview of bench basics.

Remember, work isn’t school. If you don’t recall/understand something you can take a little time refreshing on the material before undertaking a project/analysis.

I have a little secret :) We didn't cover vector spaces yet. I know horrific, but that's it. Another secret is I already saw a proof of each problem. We are studying out of Henry Ricardo and just finished the section 1.3. Haven't even covered the bases yet. These exercises are supposed to give a taste for what's to come. But your attention is flattering :)

Haha I mean he literally did. Go check it out on Amazon

Here is a cute article by Terrence Tao on gauges:

https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/

A gauge transformation is essentially a change of coordinates which is usually done to simplify whatever problem you are trying to solve. These "coordinates" aren't your usual x, y, and z, but something a bit more abstract, but still can be understood geometrically. I find it unfortunate that E&M textbooks don't discuss the geometry of gauges... I like "An Elementary Primer for Gauge Theory" by Moriyasu:

https://www.amazon.com/Elementary-Primer-Gauge-Theory-Moriyasu/dp/9971950944

http://www.lulu.com/spotlight/jed_mcclure

https://www.amazon.com/Hexagonal-Graph-Paper-Notebook-Notebooks/dp/1537648705

Whatever happened to the Metric System is a really interesting book that goes through the chaos prior to "metrificiation" during the French Revolution, and the scope of the craze around unit of measure standardization, including descriptions of the calendar system that was put in place. It's a surprisingly engrossing book.

I have always been fond of Probability and Measure by Patrick Billingsley.

Measurement

http://www.amazon.com/dp/0674057554

I understand the techniques proposed by Lockhart, and he has a good book out Measurement that illustrates some of his techniques.

I'm trying to address the same problem in a fundamentally different way. There are elements of discovery in my stuff, but it is more focused on presenting the development in a historical context.

Lockhart's method is great for high school students who have a teacher devoted to the method and who is steeped enough in the mathematics to lead the discovery. I think there is value in both.

Clearly this issue is not easy or straightforward. My advice going forward is to either a) give us a more detailed look into your data set or b) delve into the primary literature. Many sub-discipline journals will publish applied statistics articles that could perhaps pertain to your circumstance. I advocate the latter because this will give you an idea of how members of your field have dealt with this problem. The Web of Science is a great search engine for this. I also found this book on regression and heteroscedasticity (I've never read it btw).

[Measurements and their Uncertainties: A practical guide to modern error analysis] (https://www.amazon.ca/dp/019956633X/ref=cm_sw_r_other_apa_voMMyb7ZW9FSH) is what I used for my experimental physics course. Together with Taylor it seems to make a good resource.

The US does use the metric system. Did you know the US was the first country to decimalize their currency? We use metric everyday, but we also use older units. There are many very good reasons for this.

http://www.amazon.com/Whatever-Happened-Metric-System-America/dp/1608194752/ref=sr_1_1?s=books&ie=UTF8&qid=1407338001&sr=1-1

To really get a good feel for how big stuff really is on comparison, I recommend The Measure of the Universe by Isaac Asimov.