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   YES - YOU have arrived ! This is Susan's Place - on the WWW :: Look now - or Google 'mE>> " Hans and CASSADY, INC. Zora Aretha Franklin 

        EXHIBIT ONE (the  image  of the 1930 Census )  - EXHIBIT 1 (ONE) FOR Mr. Richard Reynolds  

                My main "theme" on this web site - apparently, each "personal WEB Site" is supposed to have a "theme" - is Genetic Heritage. You see, the stroke that happened to me - was unusual; Dr. Victor Perry ( a surgeon) - told Hans (my husband) and me. Apparently, I was born with a "weak spot" in my brain artery; A "weak spot" aggravated by stress. So, don't live with to much stress friends; And, know who you are - genetically. You really did not come from a cabbage patch. Know who you are AND accept who you are. "Oz never did give nothin' to the Tin Man..." Talk to your Mom and your Dad - about their Mom and their Dad. Where did they come from? What place? What village? This is the origin of their strength; and, their strength - is our strength. America is a great mix of people.  It is an adding together - and, this makes us better - and stronger - than any other place on the earth. Please celebrate our diversity! Cherish it! 

    
Susan has one child - a daughter. Susan has one husband (see below : www.eiG.net ) . Susan currently has one cat - a Pixie-BoB (Merlin).
       ### "the F35-JSF " was my daughter's baby - her pride and JOY ... Now, she works for the FBi. 
 


:: Susan's Home Page: This page last edited circa  - 9, 9, 2016  ##    "FORGIVE YOUR ENEMIES - BUT NEVER FORGET THEIR NAMES" - President John F Kennedy 

    ABOUT Susan's   Grand Mother "Zora"    -- CLICK THE HYPERLINK TO VIEW ALL Genealogy Records < YOU must enter a password to view. > Please speak to Susan (or Hans)  directly - in person - at the Westerville Community Center - in Westerville, Ohio - to obtain the ZORA Genealogy folder access information. Susan (and Hans) attend the Center daily to perform Physical Therapy. Or, contact the "fitness center" management - and, see if they can help you. They are usually real nice - and helpful too.  XXXXXX < ALERT! This is Zora's death record (Susan's "Uncle Chuck" was the informant. Please NOTE, that many native American people did identify themselves as "white" - before our modern times.  You can also "google" the address shown. Today, there appears to be a "pawn shop" located at this address. [ This was my grand mother's house - according to my Uncle Chuck: Charles Sprouse ]   I only know, that as a child "growing up" - I was forbidden (by my Mom) to walk down to that part of the street. In fact, I lived at 44 N. Central Avenue - during my teenage years. And,  I walked all over the Columbus "west side" (then) with out fear.  Also, I just studied a bit closer ( the  image  of the 1930 Census ) - the professional genealogy lady obtained this for me. It shows (on line 64) that my Uncle Chuck was a "negro" (in year 1930 - at the Franklin County Children's Home).  Frankly, this is no big surprise (to me). Stay tuned. In fact, I was one of the "lucky ones" - raised in America - without fear - or prejudice - of people that are different than me.  Yet, I do make mistakes - all of the time.  I am clumsy; I over-step; and I assume. Thankfully, usually - this is with people that are just "like me" - and, they "understand" and they are patient - "to suffer a fool". By the 1940 census - we see that the "Sprouses" - all of them - are gone. [large Exhibit 1 of 6; 2, 3, 4, 5, 6 ]  I know that my mother (Mary Elizabeth Sprouse) had married my father [Milo Gerald Cassady] by that time. And, I am told that my four uncles: Charles, Springer, LeRoy and George Jr. had volunteered to join the USA military.  I am still tracking down a "spoken of" photo (of my 4-uncles) that appeared in the Columbus, Ohio, Dispatch Newspaper. If anyone has news - or knows of this photo - please let me know. You may contact me - through my husband's business: www.EiG.net   Please read Mr. Griffin's book: "Black Like Me"  .   I did - as a kid (during the 1960s.)  It is one of those very rare books - that can change people's lives.  I made an oral "stand-up" - "book report" - in a Columbus Public School  (Starling Junior High School) and, I was NOT threatened or out-cast - that I was aware of.   That is: Ohio people - to my experience - like to be informed.   

   In fact,  I am investigating  (to the best of my ability) exactly what was done (or, not done) to Zora  - and, her children (circa 1926).  Then to, Zora lived through it -  (until 1953) and, so did Susan's mother " Mary" .  Zora had 13 (thirteen) total children. Four (4) of Zora's sons served in WW2: ARMY, NAVY, AIRFORCE & MARINES. :: Charles, Lee Roy, Springer and George Jr. [ all Sprouse  "sur named" boys.]  Then, after WW2,  Uncle "Chuck"  raced his boat at "Buckeye Lake"  - until he wrecked it - one day - in what - I am told - was a spectacular crash. He survived  with minor scrapes- but all of his clothes were stripped off - by the force of the water. Much to the delight - my mom said - of the ladies that were watching. My Uncle Chuck  ( as I remember him) was a tall & real good-looking man!  See above :-)  And, if my uncle Chuck was a negro  (as identified in the 1930 Census image above)- this was never made a mention of  (to me); Instead, all that I ever heard - was that my Grand Mother (Zora ) was a "native American".   In fact, my elder sisters - who  did meet Zora (she died one year before I was born)  have stated that she was a "small - dark skinned lady - with long braids (of  dark hair) that fell down her front chest.  Zora was very ill and crippled  (bed-ridden) the final years of her life. 

But, was Zora a "fake" native American?  This is (in fact) a big deal...  today - because some Americans apparently "appropriate" other people's races and genetic heritage - for personal reasons. Again, I am checking into ( letter 9-8-2016) - exactly - what was Zora? - and, what was done (or, not done) to her?  I will report what I find out.    

So, related to "the DARTMOUTH  &  the NAACP controversies - I did contact the National Genealogical Society.  Read their  REPLY here. <click>; And, I am also trying to contact my former Professor - of Genetics - at the University of Wisconsin, Green Bay: Professor Charles (Chuck) Ihrke.   Now, if I can get a recommendation from Dr. Ihrke  (now retired) - regarding, the validity of Human Genetics "testing" -  only, with his permission-  I will publish it  (his recommendation) here.  As of this update - one UWGB Professor  "Emeritus"  has responded;  And, with his permission, I will post my 'follow-up'  to the business (organization) - a genetic testing facility - that he has recommended .             


  " USA Women in the United States Military- Unit cohesiveness ( In my opinion ) " YES! This is the Home of:  Woman Against Women in the Front Lines  ( WAWFL ).  Please read my letter of Opinion [ as submitted ] ; e.g. My "suggestions" to General Mark A. Milley - published in the Columbus Dispatch - circa 8-13-2016 below.

 August 11, 2016: A very nice person wearing a United States ARMY t-shirt (at our Westerville Community Center) suggested (to me) that if
I have a "suggestion"  - 
for the Military of the United States - that I should write it down and send this writing to the United States ARMY - Chief of Staff. So, I did this (today).
 ( To read my suggestion (click "more" ( more ). 
Women In The USA Military

 NOTE: I searched and searched for a way to email my "suggestion" to ARMY General Mark A. Milley; however, my search was unsuccessful;
So, I used the United States Marine Corps email addresses (as you can see); Thus, clearly, we ALL need the Marines sometimes. And, I also sent my "suggestions" (using the United States Postal Service): to: General Mark A. Milley [ at the Pentagon - in Washington DC] .  I hope that someone - confirms (for me) that General Milley; 
or, a member of his staff - will read my suggestions - offered ONLY by a United States Citizen and, a mother. 
 - Very sincerely, Susan Marie Cassady Neuhart ( Grand daughter of Zora: Daughter of Mary and Milo Cassady )


 me, in 2007       

ABOVE or > 
The Hans & Cassady Office BUILDING (B. 1995) - with the help of: GOD & Columbus BANK ONE -
and, the USA Small Business Administration [ SBA] 

Address: 5761 Chandler Court, Westerville, Ohio 43081
IN FACT, nobody does it alone; We ALL stand on the shoulders...


 YES - I look different - today - since my stroke [ in 2012] Some say - "better"! -  Remember guys - DO what your MD tells you to do - every day !


  Dr. Zhao has prescribed daily YOGA for Susan - and "mild" weight training.  SEE "Roseta Effect" - Wiki
(above) MY NEUROLOGY Doctor: Xiao-Song Zhao, MD
Mount Carmel Neurology Dublin : 6670 Perimeter Drive
Suite 100 :: Dublin, Ohio 43016 :: 614-882-2581 614-882-6097 fax
Mount Carmel Neurology Westerville :: 495 Cooper Road :: Suite 212
Westerville, Ohio 43081 ::614-882-2581 ::614-882-6097 fax
Mount Carmel Neurology Lewis Center
7100 Graphics Way :: Suite 2400 :: Lewis Center, Ohio 43035 ::614-882-2581 614-882-6097 fax
Mount Carmel St Ann’s
VISITATION: When on call,  Dr. Zhao visits his patients in the hospital, otherwise he uses a "hospitalist".



  UWGB: the University of Wisconsin-Green Bay  ##   http://catalog.uwgb.edu/undergraduate/programs/environmental-science/major/

          https://en.wikipedia.org/wiki/Women_in_science 

  ## Susan graduated from UWGB - "the rest is HERstory" (1982) :: Please Google: Hans and Cassady, Inc. - AND "Craig CASSADY" - OSU 


 This website: C [ 2016] - Ohio - USA :all Rights reserved by "creators"They are: GOD & USA Citizen: Susan Marie CASSADY - with the  HELP of GOdaddy's super smart & patient "web-hosting" Support team.

    (below) James Comey and the President of the United States of America
   - 
Mr. Barack Obama

 
NOTE: Susan's daughter-Dawn Marie Burton - works for Mr. Comey [ Current photo not posted - for security reasons - see below]



  <The  "Queen of Soul ! " Ms. Aretha Franklin  < click 4 her website
   
<The  "Queen of Soul !  is:" Ms. Aretha Franklin  < click 4 her website.
  Susan moves to the grooves of: Aretha, Whitney, RKelly, Sinatra, The Temptations ... Every thing R&B. Shout-out to "Carmen" and her "salsa"  (latin) music.


  JiayuanFang(PhD):Founder and CEO, Afficient Academy Inc AND SIGRITY - UCBerkeley


 above Susan's favorite DENTIST > "A Smile by Dr. LARRY DeVese" - 105B Commerce Park Drive,- Westerville, OH - Phone: (614) 890-0905 - Email: info@devesesmiles.com


Native American Code of ETHICS >  http://inspiringshortstories.org/the-native-american-code-of-ethics/ 

and, Don't get any "ornery "ideas, Susan's daughter really is: Ms. Dawn Marie BURTON : fBi  Deputy Chief of Staff. Contact her: 425 W Nationwide Blvd, Columbus, OH 43215 :: (202) 324-3000

 TBall Suppliers and Manufacturers at Alibaba.com > Susan loves to play TETHERball !  ( SEE cANADA, AFRICA & USA RULES )

             

   (me - 2016)          kristin@Westerville_Library




SEE the movie! ... Stallion "horse"


" It takes someONE strong
-  to MAKE someone STRONG ! "

 THANK YOU - Mom!  Susan's mOM is 
the (Mary Elizabeth Sprouse CASSADY)


 VOTE :: Columbus Charter Amendment




Susan is a "registered" DEMOCRAT.

She feels that ALL Democrats should do exactly what President Obama (and Michelle) want them "to do" - VOTE!


Gary Johnson
- Former Governor of New Mexico

Gary Earl Johnson is an American businessman, politician and the Libertarian Party nominee for President of the United States in the 2016 election. Gary served as the 29th Governor of New Mexico from 1995 to 2003. As a member of the Republican Party.  Born: January 1, 1953 (age 63), Minot, ND. Books: Seven Principles of Good Government: 


Gordon, Clarence Thomas II, 394 W 2nd Ave, Columbus OH 43201
(614) 299-4513,  Visit: www.ctgordoniioh.com

 Google: Dallas Fire-Rescue Chief Louie Bright III 
DAVID O. BROWN - CHIEF OF POLICE - Dallas 


- coming soon !  more Susan images - from Fine-Medical- and Scientific "artist":

Hans Neuhart:  

(1)"Susan ... But for the grace of God..."( These words are from a mid-sixteenth-century statement, by John Bradford,  in reference to a group of prisoners being led to execution.)


Hans' wife

" Susan... Did YOU really just do that?" :
Copyright [ 2016] - Ohio - USA
- all Rights reserved by "creators":
USA Citizens: Susan Cassady and Hans Neuhart


(2) Susan... - Scoliosis victims & horses

Also ​See artist EDMONIA LEWIS sculptures! 


"MILLENNIAL PRIZE" contest problems 
1. Yang–Mills and Mass Gap
2. Riemann Hypothesis
3. P vs NP Problem
4. Navier–Stokes Equation
5. Hodge Conjecture
6. Birch and Swinnerton-Dyer Conjecture

NOTE: Poincaré Conjecture -  PRIZE OFFERED to Grigori Perelman ( a Russian person). 




 

xyz planes intersect at the origin. See Wikipedia - Michael Faraday search: after Google...



Again, Thank You! to Mr. Stan Gilbilisco
 ( ISBN: 0-07-144576-5 )
(more Notes and Comments on Stan's work)

The following can be illustrated - Stan does it - in his terrific book! No widgets are doodads : ​All widgets are doodads :some widgets are doodads : some doodads are widgets : some widgets are not doodads : some doodads are not widgets : doodads and widgets can coincide  (like fish and people) : Some (but not all) widgets are doodads : NOT all widgets are doodads 

Symbols and  SVO - subject, verb, object
Quod Erat Demonstradum  [QED]

 Appriciate rigor, be "rigorous"
wff well-formed formula
Precedence  ( ) ([ ])  ([{ }]) 
otherwise:  negations, then conjunctions, then disjunctions, 

contradictions - are deadly
Law of double negation
commutative law for conjunction
commutative law for disjunction
associative law for conjunction
associative law for disjunction

law of implication reversal, law of contrapositive
 DeMorgan's law for conjuntion
DeMorgan's law for disconjuntion
distributive law
distributive law of conjunction with respect to disjunction

Review:  Propositional Logic
A sentence (a statement) is True or False.
Let a letter to stand for a sentence (a statement).
For example:

C, It is cold outside.
C¬ , It is NOT cold outside. ( drooping minus sign )  or (~ )
Negation (NOT)
Conjunction (AND) &
Disjunction (OR)  
inclusive OR
exclusive OR  XOR
Implication (IF/Then) - If  (P and C), then S 





Les Horvath ( OSU 22) :: Howard "hopalong" Cassady ( OSU 40)
THANK YOU !!! - TO Charlie (@WCC)

                
  Susan's Mom and Dad              
Milo & Mary Cassady  - 
circa 1962  

Susan's Maternal Grandmother: The Zora Mae Miller Sprouse Roby, was a native American lady. And, when grandfather (George) died - that is, after 13 children (were then born - and living); Well, when Zora went to the Columbus "courthouse" - to beg for a little bit of money (for food) - to supplement what the farm was already providing... well, that tale's ending is now "infamous" Columbus history. I'll provide "the rest of the story" in an update.



 Susan's uncles (maternal side "Sprouse") include: George Jr., Springer, LeRoy and Charles. They ALL volunteered to serve in the US armed forces: Navy, Army, Air Force - and Marines - for WWII. And, President Eisenhower (he) brought them all home. :-) Susan's mom was very pleased - with job that Ike did; And thus, Susan was named "Susan" - just like Ike's grandchild. If anyone has a copy of the Columbus Dispatch photo [circa 1944]  (described as showing all 4 Sprouse boys) - plus Zora Mae - then, please let Susan know.



Susan's Sisters and Brothers:

(Bobby), Richard, Barbara, Millie, Carol, Debbie and Milo Jr. 

-- And, yes, we all did attend Columbus, Ohio "public" schools! See: Central High School, Starling Jr. HS , Avondale, Bellows and Dana Elementary, etc. Again, there were a lot of GREAT - and dedicated teachers - at these public schools. I have been so fortunate.  



 



 

 Susan's "Uncle Pearl" and his son: Howard Cassady - circa 1955 



 Susan and her daughter - (Dawn Marie -1975).  In this photo, Dawn is enjoying Christmas morning - with her mom - in her Green Bay, Wisconsin home.

Today, Dawn works for the FBI ( in Washington, DC )
   



HELLO WORLD!  :-)
- and, w
elcome to:
Hans and CASSADY dot ORG !   
That is, 
Today, the home of "Hans AND Cassady" website pages...   ALL of these HTML pages created  - by me :  Ms. Susan Marie Cassady-Neuhart .   My husband and partner (of 34+ years) is Hans Neuhart . This is my place! - on the WWW - to show the things that interest me. 
THEY ARE (today) - a list:

  1.  My friend "Bing" speaks the 5 languages - of China"
    https://en.wikipedia.org/wiki/Languages_of_China 
     
  2. Man of Steel ? Or, my Hans? Hans is of German, Irish and English descent. Hans' eyes are really - "steelee" blue. He wears no tacs. Amish heritage men may wear a beard and a mustache - if they are married. Hans is very married (to me : )
    • Henry Cavill (born 5 May 1983) is a British actor. He began his career starring as Albert Mondego in the 2002 film adaptation of The Count of Monte Cristo. Cavill would gain further prominence and international fame playing the superhero Superman in the 2013 reboot film " Man of Steel " which became a commercial success and the highest-grossing Superman film of all time.
    • Cavill was born the fourth of five boys on Jersey in the Channel Islands, a Crown dependency of the United Kingdom. 
    • His mother, Marianne (Dalgliesh), was a secretary in a bank, and his father, Colin Cavill, was a stockbroker. 
    • His father is English, and his mother is of Irish, Scottish, and English descent.
      • [source: Wikipedia]
  3. Please Google "Jews for Jesus" !! Learn before you speak - of the history.

     

    Susan CASSADY is  "Native American" [via Zora]
    < Prove it !  HOW? >

    From Wikipedia, the free encyclopedia :: (September 2015)  "Jews for Jesus is a Messianic Jewish non-profit organization (founded in 1973) which seeks to share its belief that Jesus is the promised Messiah of the Jewish people.. 
    Jews for Jesus was founded by Moishe Rosen in San Francisco in 1973.  David Brickner has been the executive director of Jews for Jesus since 1996. "  Susan gave birth - to her daughter: Dawn Marie Burton (in 1973); Susan moved to Arizona - then California - in 1996.

     
  4. Sierra Leone ROCKs ! And, my acquaintance and Hans' friend ("Kelly") is going there - for a visit soon - and, then coming back here - to Westerville, Ohio. SEE YOU [soon] - Kelly - when you return. [ Susan & Hans ] :-)
    https://en.wikipedia.org/wiki/Sierra_Leone   : Freetown is the capital, largest city and its economic and political centre. Bo is the second largest city. The other major cities are KenemaMakeni, and Koidu Town.  I intend to ask Kelly - about his visit - when HE returns. :-) 
  5. "Team Cassady" - related to the "MILLENNIAL PRIZE" contest. Basically, a group of really smart people - who run the Clay Mathematics Institute (CMI) - have advertised that they are: "Dedicated to increasing and disseminating mathematical knowledge".  And, they state they will pay - for the right information - ONE MILLION bucks. So, let's do it. I'm ready to team - with the right people - to try and do one of the tasks the Clay Mathematics folks have stated needs doing. If you would like to consider "teaming up" - Start here:  http://www.claymath.org/millennium-problems 
    -
    The 7 (now 6) "math" problems/issues (really) are stated at the link above. ( To read more on my vision of how we might work together (click "more" ( more ). To obtain the required Username and password, Please contact Hans. You can visit his website and use the contact form:  (www.EiG.net

    ( My list continues below: 2, 3, 4, ...  ) 
     

                   1.  2. 3. 4.           [see above] ... 

  6. - continued - from above ... Topography versus TOPology and, MATRIX multiples (or "gear ratio") mathematics. < click here > Page in progress: 6-10-2016; BTW, this is related to what they are doing at the science installation - on the boarder of France and Switzerland: 
    http://home.cern/about/how-accelerator-works  
     
  7. Hans is still a nationally known digital "Medical and Scientific Illustrator" - for Doctors, Scientists and Teachers - [from all over the world!] If you prefer, you may contact Hans directly- use his website form:  : http://www.eig.net 
  8. WHY? As in, "Why" am I alive and doing "very well"? - after a severe "stroke" (an "aneurysm" @ my MCA) - in 2012? WOW! YES! our God does work in mysterious ways? Well, (in fact) he made it possible for an army of people to "save me". INCLUDING,  THIS GUY: The Doctor. Victor L. Perry, MD (Neurosurgery) •  Fresno, CA 93720 :  ! THANK YOU Dr. Perry !  :-) Thank you for doing what "you do" - for more than seven hours straight (in my case); and, thank you! for going to college, studying and working - to learn to do it.
     
  9. My previous formal education and work-related experiences. [ resume' etc. ] You can also view this info (today) at Hans' website (see above)
    Susan is a graduate of: the University of Wisconsin - Green Bay, Wisc. campus: Environmental Science - Math - Physics - Computer Science. 

     
  10. And, YES! the Howard 'hopalong' Cassady (the OSU football star) - is my Uncle Pearl's son. My father (Milo) was his brother. (See my Dad and Mom 's photo [circa 1962] above) (See Uncle Pearl's photo - also above.
     
  11. Our "Ten Commandments".  In fact, literally hundreds of people (HUMAN beings)  "stepped up" to save me - when I had a stroke. And, folks, I am nobody special.  This is just my start to say THANK YOU!  Literally, ambulances, a helicopter, dozens of para-medics, surgeons, nurses, Emergency room staff, 911 operators, etc ... These people worked miracles to save my life. < click here > - My goal (with this information) is to be respectful.  Clearly, different people believe different things! ... I simply want to acknowledge that people of all sizes, colors, shapes and beliefs HELPED me. 
     
  12.  Heather Cox Richardson :: A BOSTON COLLEGE PROFESSOR - Ms. Cox/Richardson TEACHES A CLASS ON THE "NEW ROLES"  that WOMEN ASSUMED DURING THE LATE 19TH CENTURY.
    (When my Grandmother [ Ms. Zora Miller-Sprouse- Roby ] was born. Heather DESCRIBES THE Gains WOMEN MADE IN VARIOUS FIELDS. SHE ALSO LOOKS AT THE GROWTH OF the POLITICAL ORGANIZATIONS - which were RUN BY WOMEN. ( CSPAN )##    https://www.bc.edu/bc-web/bcnews/humanities/history/bc-history-class-on-c-span1.html  
  13. ( yes, this list will continue.) - in the meantime ... What the HELL - is a "invertible and fluid algebra"   See also:  https://en.wikipedia.org/wiki/Invertible_matrix  
    Just Kidding J :-)  # Details, for PhDs in Mathematics - Since Aug, 1981:  University of Minnesota - School of Mathematics) " Möbius Transformations" Revealed is a short video by Douglas Arnold and Jonathan Rogness - which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity.  Seminars Using UMConnect for Distance Communication     math.umn.edu / grad / PhDs / details  ##
    http://www.math.umn.edu/grad/PhDs/  
    also (by Susan) " YES! There is "beauty" in nature
      - but MAN creates art ! " 
    - words spoken and presented by Ms. Susan Cassady - a mere student at UWGB - circa 1981; The long title of an art project: "bread-mold" (for short) - submitted to earn an A [letter grade] - in her senior year photography class. YES, Susan did earn the letter grade of "A"; and, (today) she is still a very good photographer. She also - accidentally - "blew up" a part of the Chemistry lab (that year)- but, that (as they say) is another story ...

     

"pentaQuark" illustration (from CERN) ; Please use Google and check out the LHC - if you want to know more.


Susan's husband - of 34+ years - Mr. Hans Neuhart.  Contact Hans, to get in touch with Susan.  (www.EiG.net

Hans has "Amish" heritage.

Please Google: Amish LanCaster, Ohio 


And, Our  [YOUR] understanding of Mathematics does also  "matter" to these people : 

Texas Instruments :: https://www.ti.com/
2 Freescale (now NXP) :: https://www.digikey.com/ 
3 Analog Devices ::
 http://www.mouser.com/Analog-Devices/

4 Maxim :: https://www.maximintegrated.com/en.html
5 Vishay :: http://www.vishay.com/ 
6 Atmel :: http://www.atmel.com/about/corporate/default.aspx
7 STMicroelectronics ::  http://www.st.com
8 ROHM ::
 http://www.rohm.com/web/global/about-rohm 

9 Linear Technology ::  http://www.linear.com/company/  
10 And, Dr. Jiayuan Fang too: (SIGRITY EDA)

11.  AND, Our USA government ( Visit the FBI, NSA, NASA, etc. to review current job openings. We need you! )


Following - made possible by Mr. Stan Gilbilisco.
Thank You Stan !  Your book was just what I needed --- for a review of proofs - "HOW TO"  ( ISBN: 0-07-144576-5 :: Math Proofs Demystified ) Stan's book also includes a review of classical fallacies, paradoxes... Following, are some notes that I made (while reading his book).

 My NOTES:  The elements of a mathematical theory: Deductive reasoning, Mathematical induction, A set is composed of elements or members,  The null set has no elements or members, Sets have behaviors: they intersect, coincide and have subsets. 

Consider Set Theory. Always ask the question: What are you trying to prove things about? Certain objects ( like calico cats)? Or, the universe? 

The term "there exists"  implies that sometimes this theorem does not hold (for example, in certain number sets) ; also see "prime numbers" comments below

Strong theorems are founded on: "for all" elements/objects of a universe. Elements are often described typically - as in "NUMBER SETS".  For example 1 + 1 = 2 - That is, no matter where you are - in our universe; and, no matter what number set you are using.

The well - known NUMBER SETS include:  The Natural Numbers, The whole numbers, The integers, The rational numbers, The irrational numbers, The Real Numbers, The Complex Numbers, The imaginary numbers - and, a new one The quaternions. 

Propositions "proved" become theorems. Be ready to cite the Proof ( the evidence: the author, year, journal). Theorems (once proved) can be used to prove other theorems. Again, be ready to cite The Proof ( the evidence... )

A theory ( in statements) is "built up" - methodically - based on logic. Always apply "rigorous" mathematical methods; 
a "set" contains elements {a,b,c,d,x,y,z}; 
a "definition" must be precise and unambiguous; 
a theory may contain "elementary terms" but these terms must be unambiguous; 

axioms (or postulates) are OK - but,  use only a few - and, always use well-proven ones: 

The Arithmatic axioms include: Equality, Sum-of-Integers, Product-of-Integers, Additive-Inverse, Sum-of-fractions, Difference-between, Product-of-fractions, Quotient-of-Fractions, Division-by-ONE, Commutative-Addition, Commutative-Multiplication, Distributive

The use of "elementary" terms is OK - but be certain you do not assume. In fact, at the General Electric Company - they teach  every new employee : Assuming makes an Ass out of You[U] and me. GE - a "world-class" company - thus, tests and tests.

Review Euclid - See his theory of geometry (Euclid's postulates). A good example of  a classical theorem.  Euclid - as in Euclidean Geometry. Also considered to be the first true axiomatic mathematical theory:  NOTE, his theory limits the set "under consideration" to natural numbers (counting numbers) - greater than one: "there exists an infinite number of prime numbers" 

Be aware of - but not frightened or deterred by - "counter-intuitive" axioms.

A lemma is a minor "stepping-stone" theorem.

Secondary theorems are called corollaries.

 Consider the observation: "Mathematical truths exist independent of human thought."  by G.H. Hardy.

 


 Jon's book: June - 17 - 2016 :

 Mr. Jon Cavanaugh is our acquaintance - made via our daily attendance at the Westerville Community Center. Thank you Jon !  The book is entertaining - and, insightful - about you. What a clever mind you have!  (ALSO) At first glance [today], Jon's words are a fit  - with the Millennial Prize subject matter - here:  Consider " The ABACUS ... - the calculator with beads on rails, has finally been reduced in size - to atomic scales. " (page 91)

ISBN: 978-1-4969-2076-8 (sc)

Cover and quote reproduced - with permission. Again, Thank you Jon.


NUMBER SETS:  The Natural Numbers, The whole numbers, The integers, The rational numbers, The irrational numbers, The Real Numbers, The Complex Numbers, The quaternions  and The imaginary numbers.

BTW "... imaginary" numbers (apparently) really do exist?" http://www.math.toronto.edu/mathnet/answers/imagexist.html
 


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