Mathematical Knowledge One Variable Equation

A one variable equation may look like this, with informnation on either side of the equal = sign.

12a + 8 = 53 – 3a

The variables can be on the left side, and the numbers on the right side.  The numbers could be put on the left side and the variables on the right side.

Variables on the left:  12a + 3a = 53 -8

Numbers on the left:  8 – 53 = -3a – 12a    ,  or  -45 = -15a

It is easier to work with positive values on both sides of the = sign when it possible.

Let’s use  15a  = 45  .  Divide both side of the equation by the number 15 .  15a/15 = 45/15

a = 3      Mathematics check  12(3) + 8 = 44.   53 – 3(3) = 53  – 9 = 44 .

Linear equations where one or more sides have a fraction.

2x + 7 =  x/4      .    The first step is to remove the fraction.

4 X (2x+ 7) = 4 X  (x/4)       8x + 28 = x   .  Move the number or the 8x to one side.

8x – x  = – 28   7x  = -28    7x/7 = -28/7     x = -4

Mathematical Knowledge Question Monomial Binomial Polynomial

Algebra expressions are composed of terms.  A term is a number, a variable, or numbers multiplied by variables.  A number such as 3, a variable can be something like 3a or 3a[superscript2]  [3 times a times a], a combination of letters representing variables such as ab .

Monomial:  an algebra expression of one term.  An example is (4 + 2z

Binomial:  an algebra expression of two terms.  An example is (4+2z + (5-2y)

Polynomial:  an algebra expression of three or more terms.  An example is (4+2z) + (5+6y) + (4-a)

Terms can be added or subtracted IF they have they same variables and the variables have the same exponents.  (4+2z and (5+6z can be added together.

(4+2z) + (5+6z)= 9 + 8z , but (4+2x) + (5+6y) cannot be added together.

Unlike terms such as a + a [superscript2]  [a to the second power], or a + b , cannot be added together.


Numbers and variables can be multiplied together and divided.

(4 + x) can be multiplied by a variable such as 6y.   (4 + x)(6y) = 24y + 6xy

Two variable can be multiplied together.  (4d)(6y) = 24dy  .  It may be easier to rearrange and separate the components of each variable, combining the numbers first and then combining the letters.     (4)(6)(d)(y)  (4)(6) = 24  .  (d)(y) = dy .   24 times dy  or using the mathematical symbol for multiplication  24 x dy , equals =  24dy .

Multiplication of bionomial and trinomial numbers (one number and two variables)

Multiplication of binomial numbers is shown first.  Use a method known as FOIL.

The capital letter X is used as the symbol for multiplication.

F is for First, O is Outside, I is for Inside, and L is for Last.

Multiplying (4 + 2x) times (5 + 6y) using FOIL  (4 + 2x) X (5 + 6y)

Multiply the FIRST part of the term inside each parentheses.  4 X 5 = 20  F for First

Multiply the OUTSIDE part of each term)  4 X 6 y  = 24y  O for Outside

Multiply the INSIDE or second part of each term  2x  X  5 = 10x

Multiply the Last part of each term  2x X 6y  = 12xy

Add the result of each multiplication   20 + 24y + 10x + 12xy

MULTIPLICATION of TRINOMIAL or POLYNOMIAL numbers.  Polynomial is many terms.

Multiply each term within the first variable by each term of the second variable.

(4 + 2n)  X  (2 + p + q)

Multiply the first part of the first term and the first part of the second term    4 X 2 = 8

4 X p = 4p

4 X q = 4q

2n X 2 = 4n

2n X p  = 2np

2n X q = 2nq

Add the result:  8 + 4p + 4q + 4n + 2np + 2nq

Here is an example of the result using n = 2 ,  p = 3 , q = 5

(4 X 2) + (4 X p) _ (4 X q) + (4 X n) + (2 X n X p) + (2 X n X q)

(4 X 2) + (4 X 3) + (4 X 5) + (4 X 2) + (2 X 2 X 3) + (2 X 2 X 5)

8 + 12 + 20 +8 + 12 + 20 = 80     (4 + (2  X 2)  X  (2 + 3 + 5) = 80

Three common quadratics

(x + y)(x-y)  =  x [squared] – y [squared]  the number 2 appears one half line above the x and y

(x + y) [squared] = x [squared] + 2xy + y [squared]

(x-y) [squared] = x [squared] -2xy + y [squared]

A perfect square number such as 4, 16, 25, 36, 49, 64, 81 in front of the x[squared] or y[squared] in a quadratic equation means that it is probably one of the three common quadratics.




Trying to answer mathematical knowledge questions

I have started helping to tutor students who are studying for arithmetic knowledge and mathematical knowledge tests.  These students need help in these areas for a variety of different tests.

Trying to find the right phraseology and wording to explain a concept is not easy.  This is the reason why there are so many different published study guides.  Each group of authors and editors is searching for the “magic wording” that will “turn on the light bulb” so to speak.    A sidebar note in an economics textbook I used in a course back in 1997 said that there were about 50 textbooks that were written to explain the basic principles of economics.

This is my attempt to explain some of the principles of Algebra and Geometry.  If anyone knows of a calculus textbook that explains calculus for to a person who got a D minus and a very low F, please contact me.   I am well beyond college, and am still looking.

ALGEBRA     Solving mathematical problems when one or more numbers are unknown.  These numbers are called variables.  Letters a, b, c, n, p, x, y, z are frequently used as letter symbols to represent the unknown number.  In some situations, there may be two numbers that will solve the mathematical formula.

Some word problems are like this:  Eddie is 4 years older than his cousin George.  The total of their ages is now 30.  In three years, how old will Eddie be?

A parellelogram has two lines that are the same distance apart and two lines connecting them.  The angle of the left side line is between 0 and 90 degree, and the angle of the right side line is between 90 and 180 degrees.  if the degree value of the bottom angle of the right hand line is X, and the angle at the top line is Y , and the degree  angle of  X is three times Y   What is the value of angle Y

Well, if I created the algebraic equations correctly,  Eddie is now 17 and George is 13.  Eddie will be 20 in three years.

The bottom angle X is 135 degrees, and the top angle Y is 45 degrees.  The lines from the bottom line to the top line  are like the   /       /     slash lines that we see in an internet Uniform Resource Locator.

My next step is to describe Algebra equations with one variable, in my next posting.




My research work on Daniel Shays (174?-1825) and the Daniel Shays Rebellion

My home town in Massachusetts is near the home town of Daniel Shays, who was one of the leaders of the insurgency in 1786-1787 to protest property taxation, foreclosures of farms, and the state government actions of the officials in Boston that affected the people of Central and Western Massachusetts.

Daniel Shays led a force of about 1200 men to Springfield, Massachusetts to attempt to seize the federal arsenal (now known as the Springfield Armory) which had 7000 muskets and 1300 kegs of gunpowder.  The state militia led by General Shepard repulsed them, and a militia force from the Boston area led by General Lincoln went after the insurgents.  The insurgents first encamped in Pelham and tried to negotiate with General Lincoln who was encamped in Hadley.  After negotiations failed, the insurgents retreated NE and encamped in the town of Petersham.  They were probably trying to return to their base in Rutland, 12 miles NW of the city of Worcester.  General Lincoln marched his militia by night during a blizzard and surprised the insurgents at Petersham.  They had not posted guards because they thought that no one would ever attempt to march at night in a blizzard.  About 150 were captured, but Shays and others escaped.  Shays eventually went to a town in Quebec just over the border line  (I think that it had an English name at the time, but now has a name that includes the words Sainte  and Richelieu in it.)

Shays and some of his party settled in Sandgate, Vermont (Bennington County).  He moved to Sparta, New York, where he died in 1825.

There are some intriguing gaps in the story about the Rebellion that I have been trying to research and fill.  Why did Daniel Shays leave his home in Pelham and go 50 miles east (2 days by horseback) to join others in Rutland?  Who recruited him?  Who provided food and supplies for the insurgents?  The insurgents encampment was at the barracks built in 1778 after the Convention Army of British General Sir John Burgoyne was moved from Cambridge to Rutland.

The Convention Army of 4to 5 thousand was causing the local firewood supply to be depleted, and was a strain on the local economy of Cambridge and Boston.  It was also thought that a British fleet with marines and soldiers might try to land and rescue the prisoners, or return them into a fighting military force.   Rutland, 50 miles inland, was considered to be a better location,

There is a place in Rutland known as Barrack Hill, fronted by Barrack Hill Road.  The U.S. Geological Survey Geographic Names Information System Feature ID number for Barrack Hill is 617546  search Domestic Names  to get to the search engine.  This system also includes several mapping systems with topographic and or satellite imagery.    Using the Microsoft Virtual Earth System a few days ago, I saw that the home of Colonel Rufus Putnam is about 1 mile east of the site of the POW barracks that were used by the insurgents led by Shays.   The Putnam home is now a bed and breakfast inn the RufusPutnamInn.

Shays met with Putnam and told him that he was not the overall leader of the movement.  Putnam had been one of Shays’s regimental commanders during the Revolutionary War, as commander of the 4th or 5th Massachusetts Regiment of the Continental Army.    Putnam was also one of George Washington’s chief engineering officers during the war.    Putnam led a group that moved to the area that is now Marietta, Ohio and settled it when it was still a frontier area.

One of the leaders of the insurgent movement was Francis Stone (1740-1802) of North Brookfield, a nearby town.  He had been a captain in the army during the Revolutionary War.  His brother was one of the militia members who remained loyal to the state.

Shays fled Massachusetts after the failed attempt to take the arsenal.  Francis Stone was able to remain in Massachusetts.

Putnam was loyal to the Commonwealth of Massachusetts government led by Governor James Bowdoin.  But what might have he known about the insurgent force assembling in his home town of Rutland, and its leadership group and those who were financing and training the force.  Did he have any information about who the leaders were, and did he send any intelligence information to the Governor or other state officers?  Did he know which members of the militia in Worcester County could be counted on to support the state government, and which members were of dubious loyalty or active supporters of the movement?

Who owned the land that contained the Barrack and other cabins on its grounds?  Who permitted it to be used as an assembly point for the insurgent force?

I know the town of Rutland parcel code numbers for the land that is found on both sides of Barrack Hill Road.  Is it possible to trace the ownership of the parcels back to the 1780s by looking at Registry of Deeds microfilms?  Could a title search company do this kind of work, and what is it likely to cost to have a deed searched back into the 1780s?

Slavery was legal in Massachusetts until several cases in 1780 by the Supreme Judicial Court ruled that it was not permitted under the new constitution enacted in 1780.  The 1790 Federal Census tallied 5,403  All other free persons and 0 slaves in Massachusetts.  Some of the “all other free persons” may have been non-white free people (African-American descent, and some may have been Native American descent in 1780.  But looking at the Heads of Families schedules for the 1790 Census show that most of the AOFP were living in households headed by a white male or female.


How many of them were owned as slaves in the same household in 1780, and then emancipated by the Supreme Judicial Court decisions of 1780?  Were they staying in the same household because they did not have money of their own to move out and buy property of their own in town or to migrate to another town.  The name of any person who was in the AOFP group was not recorded unless he or she was the head of a household.

Was resentment against the Supreme Judicial Court for emancipating slaves without compensation an issue at the time of the protests that led to shutting down sessions of the court?   I am assuming that that no compensation was made by the state government after the Supreme Judicial Court ruled that slavery was now illegal in Massachusetts.

I could go look up the Acts and Resolves of the Legislature, which are online, to see if there was any compensation.  I can also go look at copies of early newspapers which have been digitally scanned online to see if there are stories or commentaries about the effect of freeing the slaves in Massachusetts.

I am also trying to find the names of members of the state senate and the state house of representatives.  I think that these journals have been digitally scanned and put up for research on the internet.  I am making an assumption that the names of members of each chamber appear somewhere as in a list of those who have taken an oath of office.  This is another thing that I will be looking into in the future.

I know that a substantial number of members of the 1786 legislature were replaced by newly elected members in the 1787 legislature.  Who were the members of the 1780-1786 legislatures?  Did any of them win election to future legislatures?

There is a lot to research, and I have many email messages to send out to libraries and archives asking for help.

So long for now,  Tom Lindsey









My current government documents projects in my post U T Arlington career

I watch library offers lists for materials of interest to particular libraries, and notify specific libraries of the existence of this material.

I had noticed that some of the agency entries in a guidebook for government publications had a ? mark as to the last year of existence of the agency.  I am a person who likes to have database records checked and up to date, so I use information from other sources to try to find the date that the agency closed down, and the legal citation that caused its closure or relocation to another agency.     This can be easy some times, and difficult most of the time.

I was checking on one agency this afternoon, and discovered that it was now encompassed within a larger agency that had also taken another agency under its structure.  The new bigger agency has never published any publications, so most government documents librarians are probably unaware of its existence, unless they are avid readers of the Federal Register, the Code of Federal Regulations, and the annual appropriations bills and appropriation hearings of the Congress.

If any library out there is looking for someone to help prepare publication offers lists to send to their regional library or a national needs and offers lists, I can do a lot of telecommuting work for you without having to visit your library.

Contact me using my email addresses.  I am also found on LinkedIn and Facebook, but I do not check in regularly.



The “Invisible Federal Government Information” Collection is no longer in the library

Back in 2011 and 2012 I created some Libguides (TM) about what I called the “Invisible Federal Government Information ” collection at the University of Texas at Arlington Library.  The collection had about 900,000 publications in print, microfiche, and sheet map form.  More than half the print collection was not included in the online catalog.

I discovered that about 15,600 U.S. Geological Survey 7.5 minute series topographic maps were not listed in the catalog, but could be found only by checking a shelf list of cards arranged in latitude/longitude order and then looking for the A1 to A8 … H1 to H8 code for each of the 64 sheets in a 1 by 1 degree square.  There were other things like this

It was never going to be cataloged in its entirety.  So my solution was to come up with a multipage Superintendent of Documents classification number listing of the major stems such as A 13 for U.S. Forest Service, C 13 for National Bureau of Standards/National Institute of Standards and Technology, D 100 for Army, D 200 for Navy, D 214 for Marine Corps, and so on up through Y 10  Congressional Budget Office.  It was an attempt to let people know whatF agencies and their publications might be available.  Used with resources such as other library catalogs which included every federal government publication in the collection, the G.P.O. Catalog of Government Publications,  the Federal Digital System , and specialty printed indexes, it was my attempt to “open up the stacks”,

I visited the library on Saturday, June 25, 2016.  The entire collection is gone  from the library building; there may be remnants left in the Library Collection Depository building.  There is no government documents librarian.

What a shame to see 17 years of your working career to have disappeared in 3 1/2 years.

Harrison E. Salisbury on how our country should conduct itself

This quotation is from a lecture by Harrison E. Salisbury (1908-1993), “The Book Enchained”, sponsored by the Center for the Book in the Library of Congress and the Authors League of America.  It was presented at the Library of Congress on September 28, 1983.

A printed copy was distributed to federal depository libraries that had chosen to receive publications in item number 785-J or 0785-J.  It has Superintendent of Documents Classification number LC 1.38: 10 .

“Let us conduct ourselves that no one may ever ask whether the Statue of Liberty still stands in New York harbor.  If we follow this course not only will we protect and preserve our own freedom but the light of Liberty’s torch slowly but surely will penetrate all corners of the world.”

A good reminder to all who live in the United States, citizens or non-citizens, in the year 2016.

Mr. Salisbury had spend a considerable part of his reporting career in countries run by Communist governments, such as the Soviet Union, the People’s Republic of China, and North Vietnam.   As an editor of the New York Times, he was also aware about other countries where “the light of Liberty’s torch” was a faint vision.




lindseyt starts blogging again!

Well, it appears that my lindseyt blog is back online after a long hiatus.  My next post will be a quote from a lecture by Harrison E. Salisbury sponsored by the Center for the Book in the Library of Congress and the Authors League of America.  The lecture was presented at the Library of Congress on September 28, 1983 .



A sample list of agency publications

This is one of the 350 plus publications lists that I have saved. I search the Catalog of Government Publications using the names of government authors in the List of Government Authors. The entries can be
edited to make offers lists for other depository libraries..

The first section is the listing. The second is an offers list to be sent to a regional depository in its desired format.

Army Ordnance Corps

1 The ordnance officer. 1989
D 105.2:Or 2

2 U.S. Army Ordnance Corps. 1997
D 105.2:OR 2/2

3 Serving the line with excellence : the development of the US Army Ordnance Corps, as expressed through the lives of its chiefs of ordnance, 1812-1987, with a short sketch of the history of Army Ordnance, 1775-1987 / 1987 Sterling, Keir B. D 105.2:Se 6

4 Ordnance Corps. 1985
D 105.9/2:220-1

5 Ordnance Corps : 174th anniversary / 1986
D 105.9/2:220-1/986

6 Ordnance (Aberdeen Proving Ground, Md.) 1987
D 105.29:

7 Ordnance magazine (1983) 1983
D 105.29

The list above is reaformatted into the desired offers list format of a regional depository library.

D 105.2:Or 2 The ordnance officer. 1989

D 105.2:OR 2/2 U.S. Army Ordnance Corps. 1997

D 105.2:Se 6 Serving the line with excellence : the development of the US Army Ordnance Corps, as expressed through the lives of its chiefs of ordnance, 1812-1987, with a short sketch of the history of Army Ordnance, 1775-1987 / 1987

D 105.9/2:220-1 Ordnance Corps. 1985

D 105.9/2:220-1/986 Ordnance Corps : 174th anniversary. 1986

D 105.29: Ordnance (Aberdeen Proving Ground, Md.) 1987

D 105.29 Ordnance magazine (1983) 1983

Shelflists of U.S. Govt. agency publications in Catalog of Government Publications

I am assisting a selective depository of United States Government publications assess its collection by creating electronic shelf lists of all publications since 1946. Each publication is found in the online ” Catalog of Government Publications “, httpL// .

I think that other depository libraries might be able to use these lists and the ones that are being created. Here is the text of a letter sent to the Regional Depository Libraries. I hope that my letter is clear to people who work with these publications. It will probably not be understood by most other people. Text of letter follows. Some information is edited

I am a retired government information librarian who retired [edited]. I am assisting a selective depository library assess its holdings of federal documents. The “universe “of publications are those found in the Catalog of Government Publications, , from a government agency publisher active anytime from 1946 to 2009. The range of stems is D to Y 3.Z: Y 3.2 commissions may be added later on.

Records retrieved from the Catalog of Government Publications are saved in .txt format .

The regional depository library wants offers lists sent in .txt format.

Title, Year, Superintendent of Documents Classification number .

Two sample records from the Federal Election Commission list [ Y 3.El 2/5: ] are:

55 A voter’s guide to federal elections [electronic resource] / 2010

Y 3.EL 2/5:8 V 94/2010

56 A voter’s guide to federal elections / 2010

Y 3.EL 2/5:8 V 94/2010

The numbers 55 and 56 come back with the records retrieved.

Item numbers are not included, but are available from GPO files, the commercially published Guide to U.S. Government Publications, and other sources.

I have created more than 200 lists, with more than 2.25 MB of data. My “guesstimate” is that 15,000 titles are listed. I estimate that 300 to 800 entries are added each day.

Deleting, cutting, pasting, and some typing could change a record into an offers list entry. I am willing to share my lists with other depositories.

I don’t have the Microsoft Office suite in my computer. I might be able to save the information as a spreadsheet and move whole columns if I did.

I am willing to share my lists with other depositories for their use. I can be contacted by email at
[email address deleted]

Cordially yours, s/tkl Thomas Lindsey

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