Younger humans, Montgomery College students who have attended some of these meetings: Alpha Bada, Ian McIntire, Lorena Aries, Georgio Mori-Block, Ahadu Tilahun, Daman Camara, Leah Gold, Tony Johnson, Chris Leeney, Cassidy Farrel, Brian McDermont, Eban Coleman, and on 11-4-2011 joined by Edelweiss Calcagno. These very bright students continue to move forward in their studies now mostly at other illustrious institutions (we have been doing this since 2007) with only the newer students still with us, we are a 2 year institution, but some of our bright students are with us more than 2 years, especially if they have to work full or part-time to support their studies or have three young children and a husband and household to manage.

Rules: We eat together on some Friday evening; this is a supper discussion group. Old humans (people with good jobs or retirees with good incomes) pay for their meals that we order to be delivered to the meeting room, younger humans (

Previously we have learning to multiply Multivectors (vectors) in a Linear Space (sometimes called a vector space) over a scalar Fields a Clifford Algebra. This has great application in engineering, computer science (vision), and physics. We are now studing Lie Groups as (generalized) Spin Groups Chapter 9. It is very powerful and very general and somewhat abstract. A spin group is a more generalized group than just intrinsic spin in particle physics, though this is an example of a Spin Group.

A group of files on Geometric Algebra collected by Alan Bromborsky most written by others, but some written by Alan are here. Our study guide for now is the "An introduction to Geometric Algebra and Calculus" by Alan Bromborsky now book format bookGA.pdf. Another file written by Alan Bromborsky with just the Geometric Algebra part with out the Calculus part is at file and is titled "An Introduction to Geometric Algebra." It is very similar to the first part of the previous document but it does have one diagram that is some what different on page 23 and may help some people understand the geometry in the Euclidean case. We have been applying Geometric Algebra to solve some problems, we used the document GAexamples.pdf. A file in the GA-SIG directory is GA&GC.pdf and its title is "A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald of Luther College, Decorah, Iowa so you can see these idea have even spread to Iowa. So it is time we caught up with the dark side of the moon, if they know it in Iowa, where the corn grows, then Arkansas and Mississippi, where the cotton grows, can not be far behind! What is it that we grow in Maryland besides brilliant students? This document is only 26 pages long with another 4 pages of web links and other references. It also says on the first page:

“The principal argument for the
adoption of geometric algebra is that it provides

a single, simple mathematical framework which eliminates the plethora of diverse

mathematical descriptions and techniques it would otherwise be necessary to learn.”

[9] McRobie, F. A. and J. Lasenby (1999). Simo-Vu Quoc Rods using Clifford Algebra,

Int. J. Numer. Meth. Eng. 45, 377–398.

Furthermore this is true. Another excellent review of some of
these ideas is in "Using Geometric Algebra
for Navigation in Riemannian and Hard Disc Space" which even
explains how to store these mathematical structures on a computer in
HDF5, Hierarchical
Data
Format. A new lecture "Clifford algebra: use and abuse
in physics and engineering" by Peter Renaud of the Department of
Mathematics and Statistics, University of Canterbury, Christchurch,
New Zealand, (dated 11 January 2011) that is a PDF version of a
PowerPoint can be found here.
The Moral page here is
particularly important. a single, simple mathematical framework which eliminates the plethora of diverse

mathematical descriptions and techniques it would otherwise be necessary to learn.”

[9] McRobie, F. A. and J. Lasenby (1999). Simo-Vu Quoc Rods using Clifford Algebra,

Int. J. Numer. Meth. Eng. 45, 377–398.

Some interesting articles using Clifford Algebra in elementary particle physics

- The Pin Groups in Physics: C, P, and T by Marcus Berga , C´ecile DeWitt-Morettea, Shangjr Gwob and Eric Kramerc.
- The Clifford Algebra approach to Quantum Mechanics A: The Schrodinger and Pauli Particles by B. J. Hiley and R. E. Callaghan.
- The Clifford Algebra Approach
to Quantum Mechanics B: The Dirac Particle and its relation to
the Bohm Approach by B. J. Hiley and R. E. Callaghan.

5:30PM Friday, September 14, 2007 at Mayorga Coffee Factory

6PM Friday, October 5, 2007 at ST301

6PM Friday, October 26, 2007 at ST301

6PM Friday, November 16, 2007 at ST301 directory of pictures from my crummy cell phone camera during this meeting, but very informative about what we do.

Tuesday, December 4, 2007 University of MD at College Park Physics Colloquia attended by old humans given by Sean Carroll notes.

6PM Friday, December 7, 2007 at ST301 directory of pictures from my crummy cell phone camera during this meeting, but very informative about what we do.

Noon Friday, January 4, 2008 at ST256, classes have not restarted

6PM Friday, January 11, 2008 at ST256, classes have not restarted

6:30PM Friday, February 15, 2008 at ST256

6:30PM Friday, February 22, 2008 at ST256

6:30PM Friday, March 21, 2008 at ST256

6:30PM Friday, March 28, 2008 at ST256 a directory of pictures taken on this date with my wife's digital camera.

6:30PM Friday, April 18, 2008 at ST256

6:30PM Friday, April 25, 2008 at ST256

6:30PM Friday, May 16, 2008 at ST256 after college commencement! We will decide on future dates this summer.

6:30PM Friday, May 30, 2008 at ST256

6:30PM Friday, June 13, 2008 at ST256

6:30PM Friday, June 27, 2008 at ST256

6:30PM Friday, July 25, 2008 at ST256

18 meeting completed the first academic year studying Geometric (Clifford) Algebra!

Meeting in the 2008-2009 Academic year: Year Two

6:30PM Friday, September 5, 2008 at ST256 We started on Geometrical Calculus, we only got the first two pages done so you can catch up we spent a lot of time reviewing with a new MC student Cassidy Ferrel, who is also in the US Army. Wayne Warren and Walter Faust were absent so being Faustless we also did not cover as much material as carefully as when we have Walter Faust! We had two MC students as Chris Leeney was also with us. Our leader Alan Bromborsky and our host Harold Williams is always there and Michael Brabanski and Jack Gaffey were also in attendance.

6:30PM Friday, September 19, 2008 at ST256 We shall continue Geometrical Calculus!

6:30PM Friday, September 26, 2008 at ST256

6:30PM Friday, November 7, 2008 at ST256

6:30PM Friday, November 21, 2008 at ST256

6:30PM Friday, December 12, 2008 at ST256

6:30PM Friday, January 9, 2009 at ST256 a directory of pictures taken on this date.

6:30PM Friday, January 30, 2009 at ST256 canceled on account of two essential members feeling poorly.

6:30PM Friday, February 20, 2009 at ST256

6:30PM Friday, March 27, 2009 at ST256

6:30PM Friday, April 10 (Good Friday), 2009 at ST256

6:30PM Friday, April 24, 2009 at ST256

6:30PM Friday, May 22, 2009 at ST256

6:30PM Friday, July 10, 2009 at ST256

14 meetings completed the second academic year studying Geometric (Clifford) Algebra!

Meetings in the 2009-2010 Academic year: Year Three

6:30PM Friday, August 21, 2009 at ST256 watched 1996 version of "O Brother, Where Art Thou?" and then did Geometric Algebra,

6:30PM Friday, September 11, 2009 at ST256

6:30PM Friday, September 18, 2009 at ST256

6:30PM Friday, October 16, 2009 at ST256

6:30PM Friday, November 13, 2009 at ST256

6:30PM Friday, January 29, 2010 at ST256

6:30PM Friday, February 5, 2010 at ST301 canceled College closed on account of snow.

6:30PM Friday, February 12, 2010 at ST301 canceled College closed on account of snow clearing.

6:30PM Friday, March 5, 2010 at ST301 finished through page 125! Cassidy Farrel back with us and joined by Tecola, Phineas St. Clair and Haliu Bantu.

6:30PM Friday, April 2, 2010 at ST301 a directory of pictures taken on this date.

6:30PM Friday, April 9, 2010 at ST301 a directory of pictures taken on this date.

6:30PM Friday, April 16, 2010 at ST301 a directory of pictures taken on this date.

6:30PM Friday, May 7, 2010 at ST301

6:30PM Friday, May 21, 2010 at ST301 a directory of pictures taken on this date.

6:30PM Friday, May 28, 2010 at ST301 we are really getting serious about this stuff, I know I am. Directory of pictures taken on this date.

6:30PM Friday, June 11, 2010 at ST301

6:30PM Friday, June 18, 2010 at ST301 a directory of pictures taken on this date.

6:30PM Friday, June 25, 2010 at ST301

6:30PM Friday, July 2, 2010 at ST301

6:30PM Friday, August 20, 2010 at ST301 we are taking a summer break, it is getting very hot and the room we use has the sun coming in at the wrong direction in the early evening putting glare on the computer video projectors and LCD screen in June, July, and early August. We understand projection and the obliquity of the ecliptic which caused seasons on planet earth. Full blackout curtains should have been installed in this room. We watched the first half of the silent movie Metropolis by Fritz Lang in German with Michael Brabanski translating.

20 meetings completed the third academic year studying Geometric (Clifford) Algebra!

Meetings in the 2010-2011 Academic year: Year Four

6:30PM Friday, September 3, 2010 at ST301we will watch the second half of Metropolis. A directory of pictures taken on this date.

6:30PM Friday, September 17, 2010 at ST301 we are going to start consolidation of our knowledge on Geometric Algebra.

6:30PM Friday, October 29, 2010 at ST301 we are going to continue our consolidation of our knowledge on Geometric Algebra. A directory of pictures taken on this date.

6:30PM Friday, December 3, 2010 at ST301.

6:30PM Friday, December 17, 2010 at ST301.

6:30PM Friday, January 7, 2011 at ST301.

6:30PM Friday, February 4, 2011 at ST301.

6:30PM Friday, February 25, 2011 at ST301. The Fundamental Theorem of Geometric Calculus on a manifold

6:30PM Friday, March 25, 2011 at ST301. Stokes theorem on a manifold.

6:30PM Friday, April 1, 2011 at ST301. A directory of pcitures taken on this date.

6:30PM Friday, April 15, 2011 at ST301.

6:30PM Friday, May 6, 2011 at ST301.

6:30PM Friday, May 13, 2011 at ST301.

6:30PM Friday, May 20, 2011 at ST301.

14 meetings completed the fourth academic year studying Geometric (Clifford) Algebra!

Meetings in the 2011-2012 Academic year: Year Five

6:30PM Friday, August 26, 2011 at ST301.

6:30PM Friday, September 23, 2011 at ST301.

6:30PM Friday, September 30, 2011 at ST301.

6:30PM Friday, October 14, 2011 at ST301.

6:30PM Friday, November 4, 2011 at ST301. Started recycling through the basics to make sure we understand everything. A directory of pictures taken on this date.

6:30PM Friday, December 9, 2011 at ST301 we covers some new stuff including new notation evidently invented by our leader Alan Brombosky. We did find some errors and before December 16, 2011 we are hopeful of a new bookGA.pdf. with some changes.

6:30PM Friday, December 16, 2011 at ST301 we had a new MC TPSS mathematics faculty member show up.

6:30PM Friday, January 6, 2012 at ST301 Wayne Warren returned to us after taking care of his mother in Florida.

6:30PM Friday, January 20, 2012 at ST301

6:30PM Friday, February 3, 2012 at ST301

6:30PM Friday, February 17, 2012 at ST301

6:30PM Friday, March 2, 2012 at ST301

6:30PM Friday, March 23, 2012 at ST301

6:30PM Friday, April 13, 2012 at ST301

6:30PM Friday, May 11, 2012 at ST301

6:30PM Friday, June 15, 2012 at ST301

6:30PM Friday, July 6, 2012 at ST301 postponed again!

6:30PM Friday, August 10, 2012 at ST301

6:30PM Friday, August 31, 2012 at ST301

18 meetings completed the fifth academic year studying Geometric (Clifford) Algebra!

Meetings in the 2012-2013 Academic year: Year Six

6:30PM Friday, September 14, 2012 at ST301

6:30PM Friday, October 5, 2012 at ST301

6:30PM Friday, October 12, 2012 at ST301

6:30PM Friday, November 9, 2012 at ST301 we actual started using Lecture Notes Quantum Mechanics authored Walter Faust

6:30PM Friday, December 7, 2012 at ST301

6:30PM Friday, January 4, 2013 at ST301

6:30PM Friday, February 1, 2013 at ST301

6:30PM Friday, February 8, 2013 at ST301

6:30PM Friday, February 15, 2013 at ST301 we shall omit our usual entertainment, but not study on this date because of the asteroid 2012 DA14.

6:30PM Friday, March 1, 2013 at ST301

6:30PM Friday, March 8, 2013 at ST301

6:30PM Friday, March 29, 2013 at ST301 Steve Bravy We Are those For Whom Bell Toiled.

6:30PM Friday, April 19, 2013 at ST301 Steve Bravy We Are those For Whom Bell Toiled.

6:30PM Friday, April 26, 2013 at ST301back to Quantum Mechanics with Walter Faust!

6:30PM Friday, May 3, 2013 at ST301

6:30PM Friday, May 10, 2013 at ST301 Quantum Mechanics with Walter Faust

6:30PM Friday, June 7, 2013 at ST301 Quantum Mechanics with Walter Faust

6:30PM Friday, July 5, 2013 at ST301 Quantum Mechanics with Walter Faust

6:30PM Friday, July 26, 2013 at ST301 Quantum Mechanics with Walter Faust

6:30PM Friday, August 23, 2013 at ST301 Quantum Mechanics with Walter Faust

20 meetings completed the sixth academic year studying Geometric (Clifford) Algebra and Quantum Mechanics now!

Meetings in the 2013-2014 Academic year: Year Seven

6:30PM Friday, September 20, 2013 at ST301 Quantum Mechanics with Walter Faust

6:30PM Friday, October 18, 2013 at ST301 Quantum Mechanics with Walter Faust

6:30PM Friday, October 25, 2013 at ST301 Tensors and Extensors the Multivector way with Clifford Algebra and SMPY with Alan Bromborsky

6:30PM Friday, November 22, 2013

6:30PM Friday, December 13, 2013 at ST301 "Tensors and Exentsors the Mutivector Way" with Alan Bromborsky

6:30PM Friday, January 10, 2014 at ST301 Angular Momentum in Quantum Mechanics with Steve Bravy working manuscript.

6:30PM Friday, January 24, 2014 at ST301canceled on account of the common cold in our speaker and single digit temperatures outside.

6:30PM Friday, February 7, 2014 at ST301 Angular Momentum in Quantum Mechanics with Steve Bravey moving toward gauge theory working manuscript.

6:30PM Friday, March 28, 2014 at Planetarium so we can look at two screens and two different pages at once! Angular Momentum in Quantum Mechanics with Steve Bravey moving toward gauge theory working manuscript.

6:30PM Friday, April 11, 2014 at Planetarium so we can look at two screens and two different pages at once! Gauge theory. from global to local symmetry the way mathematicians do it with Steve Bravey, the working manuscript. This stuff is real good and I used to be a Lagrangian gauge field theorist, physicist, in another life while at SUNY at Stony Brook, Dr Harold Alden Williams, before I was forced to do simpler things that were actually doable like Eulerian hydrodynamics of star forming regions and become an astrophysicist or what ever it is that I became.

6:30PM Friday, April 18, 2014 at Planetarium

6:30PM Friday, May30, 2014 at Planetarium

6:30PM Friday, July 11, 2014 at Planetarium

6:30PM Friday, July 25, 2014 at Planetarium so we can look at two screens and two different pages at once! Gauge theory. from global to local symmetry the way mathematicians do it with Steve Bravey, the working manuscript even all the Lagrangian density field theory stuff, its all written out so you will know that it really works.

Invariant TheoretInical Interpretation of Interaction by Royce Utiyama, Physical Review, Physical Review, volume 101, number 5, March 1, 1956.

Lie Groups Chapter 9 from Alan Bromborksy.

6:30PM Friday, August 1, 2014 at Planetarium so we can look at two screens and two different pages at once! Back to Geometric Algebra/Clifford Algebra the entire manuscript from Alan Brombosky. Just Lie Groups Chapter 9 and Appendix F on Direct Sums of Vector Spaces from Alan Bromborksy.

15 meetings completed the seventh year of study.

6:30PM Friday, August 22, 2014 at 12612 Springloch Court, Silver Spring, MD 20904 so we can look at two screens and two different pages at once! Back to Geometric Algebra/Clifford Algebra the entire manuscript from Alan Brombosky. Most resent version of Lie Groups Chapter 9 . Ended up celebrationg my birthday which happened on the next day; we had cake and ice cream.

6:30PM Friday, August 29, 2014 at 12612 Springloch Court, Silver Spring, MD 20904 so we can look at two screens and two different pages at once! Back to Geometric Algebra/Clifford Algebra the entire manuscript from Alan Brombosky. Most resent version of Lie Groups Chapter 9 . Ordered food, but it came late. Briefly covered the geometry of signatures see http://en.wikipedia.org/wiki/Metric_signature.

6:30PM Friday, September 5, 2014 at 12612 Springloch Court, Silver Spring, MD 20904 so we can look at two screens and two different pages at once! Back to Geometric Algebra/Clifford Algebra the entire manuscript from Alan Brombosky. Most resent version of Lie Groups as (generalized) Spin Groups Chapter 9 .

6:30PM Friday, September 12, 2014 at 12612 Springloch Court, Silver Spring, MD 20904 so we can look at two screens and two different pages at once! Back to Geometric Algebra/Clifford Algebra the entire manuscript from Alan Brombosky. Most resent version of Lie Groups as (generalized) Spin Groups Chapter 9 .

6:30PM Friday, September 26, 2014 at 12612 Springloch Court, Silver Spring, MD 20904 so we can look at two screens and two different pages at once! Back to Geometric Algebra/Clifford Algebra the entire manuscript from Alan Brombosky. Most resent version of Lie Groups as (generalized) Spin Groups Chapter 9 .

6:30PM Friday, October 17, 2014 at 12612 Springloch Court, Silver Spring, MD 20904 so we can look at two screens and two different pages at once! Back to Geometric Algebra/Clifford Algebra the entire manuscript from Alan Brombosky. Most resent version of Lie Groups as (generalized) Spin Groupy s Chapter 9 . Actually instead of studying we celebrated birthdays of two of our members, Jana Asher and Alan Bromborsky with cake and songs.

6:30PM Friday, November 7, 2014 at 12612 Springloch Court, Silver Spring, MD 20904 so we can look at two screens and two different pages at once! Back to Geometric Algebra/Clifford Algebra the entire manuscript from Alan Brombosky. Most resent version of Lie Groups as (generalized) Spin Groups Chapter 9 .

6:30PM Friday, November 14, 2014 at 12612 Springloch Court, Silver Spring, MD 20904. Geometric/Clifford Algebra the entire manuscript from Alan Brombosky with some really good figures so you can see the geometry.

6:30PM Friday, December 5, 2014 at 12612 Springloch Court, Silver Spring, MD 20904. Geometric/Clifford Algebra the entire manuscript from Alan Brombosky with some really good figures so you can see the geometry.

6:30PM Friday, December 12, 2014 at 12612 Springloch Court, Silver Spring, MD 20904. Geometric/Clifford Algebra the entire manuscript from Alan Brombosky with some really good figures so you can see the geometry.

6:30PM Friday, December 19, 2014 at 12612 Springloch Court, Silver Spring, MD 20904. Geometric/Clifford Algebra the entire manuscript from Alan Brombosky with some really good figures so you can see the geometry.

6:30PM Friday, January 30, 2015 at 12612 Springloch Court, Silver Spring, MD 20904. Geometric/Clifford Algebra the entire manuscript from Alan Brombosky with some really good figures so you can see the geometry.

6:30PM Friday, February 6, 2015 at 12612 Springloch Court, Silver Spring, MD 20904. Geometric/Clifford Algebra the entire manuscript from Alan Brombosky with some really good figures so you can see the geometry.

6:30PM Friday, February 13, 2015 at 12612 Springloch Court, Silver Spring, MD 20904. Geometric/Clifford Algebra with Alan Bromborsky.

Future dates God willing (believers in God, Gods, agnostics and atheist are welcome at our meeting)!

6:30PM Friday, February 27, 2015 at 12612 Springloch Court, Silver Spring, MD 20904. Probably Quantum Mechanics with Walter Faust.

And eventually maybe General Relativity, actually the Einstein-Cartan-Scima-Kibble Theory or really General general Relativity with Harold Williams, who knows where he is and when he is and knows approximately where and when he is going, even if no one else has a clue about him! New Gauge Symmetry in Gravity and the Evanescent Role of Torsion by H. Kleinert and Kerr Geometry as Space-Time Structure of the Dirac Electron by A.Burinskii and Time-Space Invariance and Quantum Gravity: or how c, G, and h created the fabric of the universe.

We will continue recycling through the basics when ever a new member shows up or an old member ask a basic questions. This happens about one meeting in three.

Sometime after that we are going to explore the at least three different ways of defining "Covariant Derivatives" in general coordinate transforms leading to different "General Relativities" all of the ECSKs, Einstein-Cartan-Sciama-Kibble, theories. We many even explore the case where coordinates do not commute or are small, but finite around 10^-35meters (abandoning real numbers and using finite, but large Fields, many elements in the set.). Some of us want to understand quantum gravity! Doesn't every thinking creature want to understand the origin of mass and the creation of intrinsic quantum mechanical spin in fermonic matter? I know, I do! But I also know I can't do it by myself, besides it is more fun if you do it with others. Right!!!

Links:

Linear and Geometric Algebra first undergraduate linear and geometric algebra textbook, affordable, too by Alan Macdonald.

Geometric Algebra Net at University of Amsterdam, Computer Scientist; support for the excellent book Geometric Algebra for Computer Science, an object oriented approach to Geometry

Geometric Calculus: David Hestenes and Group at the University of Arizona, Physicist

Geometric Algebra for Physicist a book by Chris Doran and Anthony Lasenby at Cambridge University

Geometric Algebra and Applications to Physics a book by VENZO DE SABBATA and BIDYUT KUMAR DATTA see URL: http://ebookee.org/Geometric-Algebra-and-Applications-to-Physics-Taylor-and-Francis-_273120.html .

Scientific Python recommended by Alan Bromborsky

Python(x,y): Free scientific and engineering development software, recommended by Alan Bromborsky

Some Video Mathematics Resources some of us have found useful

Applied Geometric Algebra by László Tisza is Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976 in MITOpenCourseware. This was found by Cassidy Ferrel, MC student participant in our Geometric Algebra Study group.

MATH E-222 Abstract Algebra by Benedict Gross, PhD, George Vasmer Leverett Professor of Mathematics, Harvard University, found by Randy Bryant.

Norman J. Wildberger's home page, Divine Proportions: Rational Trigonometry to Universal Geometry or same from Amazon.com.

Lagrangian and Symplectic Techniques in Discrete Mathematics a Ph.D. dissertation by James William Gilliam at University of California at Riverside.

Montgomery College's Planetarium home page.

web page by Dr. Harold Williams, last modified at Friday 10:13PM,
February 20, 2015.