Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Chabot Engineering Study Skills For Engineering Students Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

From CareerBuilder.com Apr08 CHICAGO, April 2008 - CareerBuilder.com's annual survey. Survey of 3147 Human Resource Professionals and Hiring Managers When asked about minimum GPA requirements: 31% of the hiring managers surveyed said they require a 3.0 and above 11% require a 3.5 and above

Robert Irwin on JPL GPA Mr. Irwin Studied Engineering at Chabot & UCBerkeley He Now Works as Test Engineer for NASA’s Jet Propulsion Laboratory at CalTech His Comments on JPL’s GPA policy: JPL has a 3.0 minimum GPA for interns and full time hires. It is a very strict policy. >>> Robert Irwin <robertirwin22@uu.vv> 8/27/2012 7:41 PM >>> ChabotENGR_Student_RIrwin_Mars_Rover_Curiosity_1208.pptx

Thank You UC Berkeley Placement Center Job Offers Circa Jan 1979 Thank You UC Berkeley Placement Center ~$70k in 2014-$

BMayer Resume Used to Obtain 12 Job Offers Circa Nov78

Study Like an ENGINEER Learning Goal Hopefully this Lecture will Help Students to Develop the Skills, Techniques, and Methods to allow Each Student to… Study Like an ENGINEER

Liberal Arts Majors Party Down

Rule-1: Be Responsible You want to be a Professional; Professionals are Expected to Assume PERSONAL Responsibility for their Actions At the University This Means Attend EVERY Regular Class/Lab meeting Be On Time, Be Courteous Complete and Turn-in All Assignments as Scheduled Ask for few “Special Case” exceptions Professors Appreciate “SERIOUS” Students

Rule-2: Mind Connected to Hand Unlike some Other Disciplines Bachelors-Degree Math and Science Education Tends to be Linear - a course will build as the Term Progresses; courses build upon each other Early Work is Required for Later Work Precise and Quantitative At Universities Most Math & Sci Courses Entail the Determination of a NUMERICAL Result There are Objectively RIGHT & WRONG Answers

Rule-2 Cont. Math & Science Education Provides Tools to Solve Problems Becoming Proficient with the Tools Requires PRACTICE, PRACTICE, & more PRACTICE Study with a Pencil-and-Paper If the Instructor Follows a Text, then READ carefully, Taking Notes in YOUR OWN HAND Work all the EXAMPLES until you UNDERSTAND them

Rule-2 Cont. To study for exams, Work problems for which the text provides answers If Solutions Are Provided to Homework or Exams, then REWORK All problems that you got Wrong Until you Understand them Neatness & Thoroughness helps A problem you solved early in the term may be needed late in the term If it’s Neat & Complete you can Use it more quickly

Don’t just READ the Text; WORK the Text Rule-2 Summarized Don’t just READ the Text; WORK the Text

Notes from EE-113 at Stanford Text Book Notes Class Notes HomeWork & Exams Go Card!

Rule-2 Personal Story BMayer Learned Rule-2 in Ted Bowen’s Physics Class At Cabrillo Community College in 1974 This TRANSFORMED My Academic Performance; leading to Results after Transfer to UCBerkeley (Go Bears) 3.8 GPA (95%) 12 Job Offers Transformed an Atty I know well from a Medium Student to 3rd out of 245 in her SCU Law School Graduating Class

Rule-3 Honor the TextBook Instructor and Class-Time provides a FRAMEWORK for Learning a College/University Skill The Text, Or HandOuts/Notes, Provides the SUBSTANCE Very Few People Learn Performance Skills by Listening to a lecture Lectures Tell you WHAT to Study The Text & Exercises DEVELOP Skills

Rule-3 Honor the TextBook From Rule-2 a Good Student will take NOTES on the TextBook in his/her OWN HAND In other words you EXPLAIN the Text to YOURSELF in your OWN WORDS

Rule-4 Listen to the Instructor The Obvious Reason → To Learn the Material The Subtle Reason → To Learn What is IMPORTANT to the Instructor What the Instructor Says in Class Gives Clues about His/Her Priorities Since you Have Finite Study Time (168 hrs per week) you need to PRIORITIZE Typically What the instructor COVERS IN CLASS will likely appear on the TESTS

Rule-5 Mind your Math & English Math and English form the FOUNDATION for College, and for Landing a good Working Position Almost all Well Compensated (i.e. Good Paying) Jobs require that the Employee be able to CALCULATE & COMMUNICATE A GOOD Employee will use ALGEBRA; a GREAT Employee will use CALCULUS A GOOD Employee will be able to READ & UNDERSTAND a written report; a GREAT Employee will WRITE the Report

Rule-5 Cont. Math & English form the BASIS for ANY Professional & Practice; c.f. Required Courses for Engineering Degrees Required Courses for Nursing Degrees Required Courses for Business Degrees Almost All Significant PROFESSIONS in the USA Depend written Math & English Doctor, Lawyer, Engineer, Business Person, Company Manager, Police Officer, etc.

Rule-6 Be Creative CREATING Something is MUCH Harder than USING Something e.g.; The difference between READING a story, and WRITING a story In the Professional World Creativity Leads to very VALUABLE outputs NEW products and/or Services Competitive ADVANTAGE SOLVED Problems

TV & VIDEO GAMES are NOT on The Creativity List Rule-6 Cont. CREATIVITY and PRODUCTIVITY are Closely Related Both Require Getting Something DONE Develop Your Creativity Thru Practice Draw Pictures Write Stories Build Things Solve Puzzles TV & VIDEO GAMES are NOT on The Creativity List

End Product of Systematic Creativity

Rule-7 Draw Diagrams for Math Science, Math & Engrng Have a HUGE Advantage Over the Written Language Disciplines – The use of Graphics If you have difficulty with a problem Chart it Graph it Sketch it Flow Chart it Diagram it

Rule-8 DON’T Sell Your Books If you follow Rule-2; then you will Build a LIBRARY of PERSONAL Reference material Since Math & Sci Education Builds, Your Text and The Study Materials associated with it are VALUABLE References Many of the Underlying Laws of Science Cross Discipline Boundaries Odds are you WILL use Your Texts as PROFESSIONAL References

Book Seller ShortSightedNess A TextBook Seller unconsciously says this to Her/Him Self: This attitude is a SELF-FULLING PROPHECY Of Couse if a person DISCARDS a TOOL, then he/she will never use it!!! I DON’T NEED THIS Anymore…

Sell Books? I don’t think so… From The Journal Thin Solid Films

Chabot CHEM-1A/B Text TSF TextBook Refs

Sell Books? I don’t think so… From The Journal IEEE TSM

TSM TextBook Refs

TextBook Refs for: IEEE Transactions on Semiconductor Manufacturing MTH1 TextBook from Cabrillo College

Sell Books? I don’t think so… From The Journal APS/AVS JVST

JVST TextBook References

Rule-9 PUT in the TIME

Rule-9 cont. From the Chart on the Previous Slide, the MINIMUM Study Hours per week 6 Hours for a 3 unit Chabot Course 10 Hours for a 5 unit Chabot Course 9 Hours for a 3 unit SJSU or CSU-EB or UCBerkeley Bachelor’s Level Course 12 Hours for a 3 unit CalPoly or UCDavis or UCBerkeley Master’s Level Course Even MORE for Ph.D or MD Level Course

R9: clueLESS vs clueFILLED Request from a ClueLESS Student I don’t have time to Study…Tell me how get an “A” AnyWay Observation by a ClueFILLED Student There is No Substitute for Personally Struggling with the Course Material

R9: You think it’s tough at Chabot… Consider this Sp10 advice from UCBerkeley Prof. Bernhard Boser to his 2nd Year, 4-Unit EE40 class “Effort: You are expected to spend approximately 12 to 16 hours each week on this course, broken down as follows: 3 hours of lecture 1 hour of discussion 3-4 hours reading (book & notes) 3-5 hours homework 3 hours labs and project” B. E. Boser http://www.eecs.berkeley.edu/~boser/courses/40/index.html

Rule-10 Study EXTRA for Exams Preparing for Exams or Quizzes requires ADDED study time beyond the 6 Hrs/Wk for a 3 unit Chabot Course Exam Study/Prep Time Guideline 3 Hours StudyTime Per 1 Hour of ExamTime

Rule-10 cont. Exam Week Study-Time Example → Chabot 5 Unit Math or Science Course 1 Hour Midterm Exam = 13 hours total 10 Hours Normal Study Time 3 Hours Exam Prep Study Time 2 Hour Final Exam = 6 hours Final-Exam Prep Time At the University Level Final Exams are 3 Hours long, which requires NINE (9) hours of Final-Exam Study time

Rule-11 Get EVERY Point If the Instructor/Professor offer the OPPORTUNITY to earn Grading Points, then TAKE IT Do EVERY Assignment Do NOT incur LATE Penalties Do Any & All EXTRA CREDIT Offerings Learn how to Earn PARTIAL CREDIT and then DO IT e.g., if SHOWING WORK earns Partial Credit, then Show your work

Rule-12 Join/Form a Study Group LEARNING a subject is one thing, TEACHING a subject is Another The depth of Knowledge required to TEACH a Subject is much Greater than that needed to LEARN the same Subject In a good Study Group ALL Students will be BOTH Learner and Teacher Study Groups need NOT be Large; two people can make an effective group

Rule-13 OfficeHrs Do’s & Don’ts DO Use Instructor Office Hours; the RIGHT Way DON’T: Walk into the Office and say: “Teach me the SAME THING that you discussed during the class I MISSED” DO: PREPARE for the Office Hour as you might for a meeting with your SUPERVISOR to make The Visit Efficient & Effective for BOTH Parties a GOOD IMPRESSION on the Instructor Helps for subsequent Letters of Recommendation

Rule-13 OfficeHrs Do’s & Don’ts Office Hour Visit Game Plan Work HARD on the Problem/Issue until you get STUCK Bring with you: TextBook, Paper & Pencil, Calculator or Computer THEN go to Office Hours and talk to the instructor saying something along the lines: This is what I have DONE so Far… Can you help me make the NEXT STEP

Rule-14: LEARN All You Can A Four-Year Degree offers the Opportunity to Learn at a Level of DEPTH & DETAIL that will Likely NOT be Available LATER in Life Higher Education In California is EXCELLENT – Take Advantage of it Study Hard; Party Later Learn Everything you Can You will NEVER regret having done WELL at the University Level

1960 CA Master Plan for Higher Ed California Public four-year Universities allow for seamless CC transfer as provided for by the 1960 California Master Plan for Higher Education. An excerpt from this plan: “The transfer function is an essential component of the commitment to access. UC and CSU are to establish a lower division to upper division ratio of 40:60 to provide transfer opportunities to the upper division for Community College students, and eligible California Community College transfer students are to be given PRIORITY in the admissions process.” 40:60 Means, for 10000 UnderGrad student unviversity, 4000 Lower Div NATIVES to 6000 Total Upper Div students. This leaves 2000 slots for CCC transfers http://sunsite.berkeley.edu/~ucalhist/archives_exhibits/masterplan/heart.html

UC & CSU Engineering Programs UC Programs CSU Programs Does NOT Include CompSci http://www.universityofcalifornia.edu/academics/engcs.html

LEARN it USE it (on the Job) Virtually EVERY TECHNICAL (and ENGLISH Composition) CLASS I took I actually USED On The Job during by 24+ Year Engineering Practice Career See Previous slides on TextBook Refs The Deeper you Learn SomeThing in the Technical & English Classes at Chabot and the University the More Likely you are to APPLY IT when you join a Math/Sci/Engineering Profession

LEARN it  Return on Investment Students are (or should be) PAYING for Their College/University Education NOT Learning DEEPLY is like Paying for a Gym membership, and then doing “Mickey Mouse” WorkOuts To Get a RETURN on his/her Educational investment the student should LEARN the Course Content NoEffort  NoGain

LEARN it  Return on Investment A excellent Perspective on RoI → “When I was a senior [in college], one of my professors asked wonderingly, ‘Why is it that you guys spend so much time trying to get as LITTLE AS POSSIBLE for your money?’” M. McArdle, “Is College a Lousy Investment”, Newsweek, Vol. CLX, No. 12 (17Sep2012)

Case Study: ClueLess  ClueFilled Consider the Test Performance Data For Electrical Circuits & Devices (ENGR43) Student The student did about 3-times BETTER on the Exam that was about 3-times HARDER!!! What PRODUCED this tremendous Improvement from MidTerm-1 to the Final Exam?

Case Study: ClueLess  ClueFilled When ASKED about the Improvement the Student Replied: >>> Robbie Sweetman <rs@zzzzzzz.com> 05/31/11 11:52 AM >>> Hey Mr. Mayer, thanks! I think I finally realized that understanding the concepts and actually being able to analyze different problems were two different things. About a week and a half before the final I started doing problem after problem after problem. I think the only way that I was able to improve in that class was by seeing a lot of different problems and FINALLY PUTTING IN MORE TIME. And to me the final [exam] was the EASIEST of all three tests SIMPLY BECAUSE I HAD DONE SO MANY PROBLEMS that I UNDERSTOOD how a circuit worked. I knew the concepts AND how they actually applied and I think that made the difference. On the other tests I knew the general concepts, but DIDN'T SPEND ENOUGH TIME applying them to actual circuits. Thanks again Mr Mayer! I think your classes have helped me REALIZE HOW MUCH TIME I have to spend when I transfer [to UCDavis in AeroSpace Engineering]. - Robbie Sweetman

Case Study: “Sac State” BSCE >>> Robert Curry 03/14/08 4:00 PM …I do have to tell you , my time at Chabot was VERY HELPFUL IN PREPARING ME to go on to Sac State. I think that ALL THE ADVICE you gave us, and the TYPE OF WORK YOU HAD US do put me in a GOOD POSITION TO DO WELL. During my first semester at Sac State, I saw a lot of OTHER STUDENTS STRUGGLING with things that I found to be familiar. Not necessarily the material, but the WORK that was required AND THE METHOD to go about learning the material. I've seen that everything that you are doing to help your students will PAY OFF for them if they choose to use it. Thank you very much Mr. Mayer. Without your help over the previous three years I don't think I would be in such a good position to succeed in my goals. Robert Curry – Chabot Transfer Student to CSU Sacramento in Civil Engineering BSCE in Dec2009 SacState GPA 3.95 Now a Civil Engineer with the California Department of Water Resources (DWR)

Comments from Former Student Mr. Nicolas Celeste transferred from Chabot to San Francisco State University; majoring in Mechanical Engineering. He eventually became the PRESIDENT of the SFSU American Society of Mechanical Engineers (ASME) Student Section What Follows are some of his comments from a Guest Lecture he Made at Chabot about his Transfer Experience

Guest Lecture by UCB M.E. Excerpts from a Guest Lecture to the Chabot ENGR10 Class made by Chabot Engineering Transfer Student (Now Mechanical Engineer) Robert Moore

Guest Lecture by UCB ChemE

Ms. Zhang Advice on Learning

Ms. Zhang notes on “Life in Chabot” Take every class seriously, especially these basic science classes like math. at the beginning, you may not see the connections between different subjects. Your goal is NOT to get an A in the class, but to LEARN something. Lecture is very important, you want your study to be efficient. THINK INDEPENDENTLY. Group study is great, but I encourage you to do the homework independently, and then you can discuss-with and compare-to classmates. Because, in group study sometimes will avoid you from knowing where you need to improve. Start early. There are a lot of advantage of starting the homework early, you have plenty of time to think, and you will have time to go to Office Hour, (OH is important in UC), you don’t need to stay up late at night and fall asleep in the other morning. For the career, I highly recommend you to look for some part-time job in the industrial sector, may be too challenging to be engineer, but try operator that require minimum course work. From your work, you can build up the network, keep good reference, update your resume. The truth is, for 2-year program, you only have one summer to look for internship. Be a tutor; it helps your UC application. Solidifies your class material. Classes completion. Because the class load would be very heavy in UC, and you need to apply principles from these basic classes in your major classes. And also, in UC, the lower division classes are lectured in huge class size, may up tp 600 ppl

Comments from ENGR Transfers Former Chabot Engineering Student George Greer Earned Acceptance into the BEST Civil Engineering Ph.D. Program on the Face of the Earth! His Comments on Chabot Engineering Chevron Environmental Engineering Scholarship Recipients >>> George Greer <g.greer03@uuu.vvv> 02/19/14 6:13 PM >>> Hello Mr. Mayer, I just wanted to let you know that I graduated from Berkeley this past December and was recently admitted into Berkeley's Environmental Fluid Mechanics and Hydrology MS/PhD program. I want to thank you for successfully preparing me for my undergraduate studies at Berkeley. I also know that the LESSONS YOU TAUGHT AND YOUR METHOD OF STUDYING AND PREPARING FOR CLASSES WILL ONLY CONTINUE TO BENEFIT ME AT GRADUATE SCHOOL. Thank you, George Greer

Comments from ENGR Transfers >>> Evan Manrique <evanmanrique@yahoo.com> 10/24/2012 10:53 AM >>> Hello Mr. Mayer,    I just wanted to thank you for the preparation you have provided me during my time at Chabot College. Getting though the first round of midterms at Cal Poly, I found myself in both of my EE classes, receiving the highest grade on the midterms. The work ethic that I had to acquire in taking your classes at Chabot has truly made me a more confident and stronger student. I hope everything is going well for you this semester and thank you again for all your help and guidance. Evan Manrique (CalPoly-SLO Electrical Engineering Student) ****************************************************** >>> dadaspeaking <dadaspeaking@hotmail.com> 10/28/12 9:50 PM >>> Mr. Mayer, It is super nice to hear from you again!! How have you been? I am using the method you taught me to study every course at Cal. I totally survived in the first round of midterms with all A's!! : ) I very very appreciate for it and again, thank you so much. Best Regards, Weida Yin (UCBerkeley Civil Engineering Student) ************************************************************************* >>> Andrew Koth <snlkoth@gmail.com> 10/28/12 6:41 PM >>> Mr. Mayor, Your tests really prepared me for the rigor of my current classes. I thought the study skills packet was particularly helpful. I hope everything is going well for you. Andrew (UCBerkeley Electrical Engineering student)

Comments from ENGR Transfers >>> Lormi Sioson <lormisioson@yahoo.com> 04/18/13 8:56 AM >>> Dear Mr. Mayer, …stay in touch with the only engineering professor that has established a good foundation of not only the material needed in the engineering field, but also preparing me for the hard work ahead. Just to update you, I was able to pass all my classes last semester and about to finish another one. Unfortunately, due to budget cuts, one our two classes here at SJSU require more prerequisites to get in and they are limited in enrollment, which has pushed me back as far as what my previous education plan was. Which is why the education plan assignment you had us do in Engineering 10 was helpful. The rigorous work required to pass my classes comes to me so naturally now because your classes have prepared me for it. I didn’t know that then and almost found it torturous, but now, I'm glad to have gone through it and it has helped me make it this far. I wanted to take the opportunity to thank you for pushing me to become a better engineer. Sincerely, Lormi

Comments from ENGR Transfers March 28, 2013 Professor Bruce Mayer Chabot College Dear Mr. Mayer: As you know, this is the first year I have taken a job as a engineering intern with Gallo Wines and this step would not have been possible with out your guidance and support. I find myself often using the advice you have given and skills you have taught in your engineering classes in my internship. Your "Rule-5: learn to Communicate" I use daily. I am required every day at Gallo to be able to communicate what I need done succinctly and precisely to my supervisors, the maintenance technicians and the machine operators. Your study skills have also been useful, especially your "Rule-2: Mind Connected to Hand." If I were to give any advice to prospective engineering majors, I would tell them take fewer units so that you have the time to work the problems out on paper. Even in my internship I have a legal pad out on my desk so that I can write out problems or brainstorm. I often use pen and paper before I use the computer. In case you were wondering, my job as a production engineering intern is to investigate and fix major problems with the bottling lines based on data. The lines I manage produce the sparkling wines (aka champagne) under the brands Andre, Barefoot Bubbly, Delicia, and Wyclef. My lines also produce the dessert wines Boones Farm, Night Train, Thunderbird, and Gallo vermouth and boxed wines Peter Vella and Carlo Rossi Sincerely, Branden Andersen

I’m Just Not at Good at Math/Sci Have you ever said “I’m just Not at good at Math (or something similar)?” If So, Please change you mind, and read below …But the truth is that everyone can become smarter at math [or sci/engr] if they practice in the right way. If a weight lifter watched other people exercise all day long, he wouldn’t get any stronger. And if someone tried to learn how to juggle by just reading a book about juggling, they wouldn’t learn. You actually have to practice the right way — and usually that means the hard way — to get better at something. In fact, scientists have found that the brain grows more when you learn something new, and less when you practice things you already know… • (See appendix for full text) http://seattlecentral.edu/faculty/jwright/math91/Assignments/due_10_03/YouCanGrowYourBrainArticle.pdf

Q&A with Math Challenged Student Q1.What do you recommend I do to Better Learn the Math needed to become an Engineer? A1. There is NO getting around the fact that Engineering REQUIRES HIGH-LEVEL Math skills. All engineers are expected to do well Math courses thru Differential Eqns (MTH4) and Linear Algebra (MTH6). Note that ALL math classes tend to BUILD on one-another; Earlier skills are required for Later classes. * I suggest DROPPING back to the level where you feel comfortable, but mildly challenged. ** Given your difficulties with TRIG (which is VERY Difficult) I would recommend MTH37; Trig/Geometric Foundations *** While taking the class **** PERSONALLY STRUGGLE with the material for about 10 hrs per week OUTside of class. **** Take advantage of the DROP-IN math tutoring available in the Math & Science Center, rm3906 **** Take advantage of the one-on-one, Appt-based tutoring in the PATH Center

Q&A with Math Challenged Student Q2. What is the fastest way to deal with this in your opinion? A2. There is NO fast way; only LONG & HARD work * To advance thru Math’s LINEAR-Course progression I suggest you plan on taking SUMMER Math Courses, at least thru MTH2 Q3. What was your approach/procedure to math in general? A3. I personally approached Math courses in the SAME manner that I did ALL my OTHER Courses (Engineering, Chemistry, English, History, etc.). This was by Studying a LOT. * Research has shown that what makes someone good at ANYTHING is PUTTING in the TIME. ** The Study Plan I used, and continue to use when I'm learning something new, is carefully described in my study skills document: http://www.chabotcollege.edu/faculty/bmayer/ChabotEngineeringCourses/All_Courses_ENGR/Study_Skills_for_Chabot_College_Students_140106.pptx

Q&A with Math Challenged Student Q4. Do you have an abstract/creative ways in approaching math? Like hand-abacus or books that incorporate all types learning? A4. What helps me A LOT is the use of DIAGRAMS or GRAPHS to the MAXIMUM extent possible. * If you have difficulty with HAND Graphing (which is BEST), then I suggest you Learn to Plot with MSExcel. ** See the ENGR25 Lectures on this topic: http://www.chabotcollege.edu/faculty/bmayer/ChabotEngineeringCourses/ENGR-25_CompMeth/E25_Lecture/ENGR-25_Lec-29_Sp14_MS_Excel-2.pptx http://www.chabotcollege.edu/faculty/bmayer/ChabotEngineeringCourses/ENGR-25_CompMeth/Demos/ENGR-25_SnCl4_Pv_Chart-Build_Tutorial_Sp14.pptx * To advance thru Math’s LINEAR-Course progression I suggest you plan on taking SUMMER Math Courses, at least thru MTH2

Q&A with Math Challenged Student Q5. How did you study Trigonometry and Calculus with Complex Algebra? A5. The Same way I studied Engineering, Physics, and everything else; by working my butt-off, and doing any and every thing I could to UNDERSTAND the course material * What engineering students study at the college level is NOT an academic exercise; what we learn in class can be USED on the JOB if we have LEARNED it DEEPLY. Q6. Did you think in mental-math or tie to abstract-ideas? A6. I don't know. I always "threw the kitchen sink" at everything I wanted to learn deeply. I'm sure I did both MentalMath & AbstractReasoning, along with ANYTHING else I of which I could think. * I would say that the more Math AND engineering I did, the more DIAGRAMS & MATH I did

Q&A with Math Challenged Student Q7. Should I do like flow charts or something or draw pictures somehow and connect visual ideas to computation somehow? A7. YES! Use GRAPHICS to the MAXIMUM Extent possible Qx. How did you study trigonometry and Calculus with complex algebra? Q8. How do I get past the math part to become an Engineer? A8. You DON"T! Engineers USE Math as a critically important part of their WORK. The use of SOPHISTICATED Math & Science is what separates ENGINEERS from TECHNICIANS. If Engineering was easy, then the profession would require such extensive training. And Engineers-to-be need to TRAIN HARD.

Engineering in the LongTerm

More Liberal Arts

LiberalArts & MBA’s

DilBert BrainStorming

Study Groups can Help All Done for Today http://faculty.evansville.edu/ck6/bstud/euler.html ".. indeed, far and away the most prolific writer in the history of the subject" writes Howard Eves in An Introduction to the History of Mathematics. Euler's contribution to mathematics is represented here by a few of the notations conventionalized by him or in his honor. Around the world, these are read, written, and spoken thousands of times every day: e for the base of the natural logarithm (a.k.a. "the calculus number") a, b, c for the sidelengths of a triangle ABC f(x) for functional value R and r for the circumradius and inradius of a triangle sin x and cos x for values of the sine and cosine functions i for the imaginary unit, the "square root of -1" capital sigma for summation. capital delta for finite difference. Euler grew up near Basel, Switzerland, and studied at an early age under Johann Bernoulli. He finished studies at the University of Basel when only 15 years old. From 1727 to 1741, Euler worked in St. Perersburg, Russia, and then moved to the Akademie in Berlin. In 1766 he returned to St. Petersburg, where he remained. But Remember YOU take the TEST; NOT the Study-Group

Book Seller ShortSightedNess A Book Seller (BSer) unconsciously says this to Her/Him Self: This attitude is a SELF-FULLING PROPHECY Of Couse if a person DISCARDS a TOOL, then he/she will never use it!!! I’ll NEVER NEED This Again…

YouCanGrowYourBrainArticle.pdf

YouCanGrowYourBrainArticle.pdf

YouCanGrowYourBrainArticle.pdf