%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This is the record of changes to files in the directory math.ucr.edu/~res/math205C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ++++++++++++++++++++++ MONDAY, MARCH 28, 2005 ++++++++++++++++++++++ At the beginning of the quarter the directory contained the following files: aaaLOGFILE The file that is now open and being read. aaaREADME Statement that files are only to be used for UCR purposes. braintest.pdf braintest.ps Amusement file to point out the need for looking carefully at questions before impulsively going in the wrong direction. NOTE. These two files yield the same output but they are in different formats that are indicated by the extensions ps and pdf. The pdf version was created from the ps version. For various reasons the ps version might have better quality in a few cases. coursehw.pdf coursehw.ps The file of homework exercises for the course. It currently covers the first two units but will be expanded during the course. geninfo205C.dvi geninfo205C.pdf geninfo205C.ps The basic information about the course: Contact information, course text, etc. lectnotes.pdf lectnotes.ps The file of lecture notes for the course. It currently covers the first three units and more will be added during the course. longcontents.pdf longcontents.ps A detailed table of contents for the lecture notes listing all the subsections. It is currently complete through the first four units. outline205C.dvi outline205C.pdf outline205C.ps A list of topics to be covered in the course with references to the course text. proper.pdf proper.ps A supplementary note on the concept of a proper mapping. The basic definition will be used in the course, but most of the rest of the material will not. One feature of this note is that it relates the different but equivalent definitions of proper maps that one sees in topology and algebraic geometry. shortcontents.pdf shortcontents.ps A one page table of contents for the lecture notes broken down into sections of individual units. sigmacompact.JPG A figure illustrating a point that arises in one of the proofs in Section I.2. smirnov.pdf smirnov.ps A proof of the basic result by Smirnov answering the following question: If a topological space has a base of open metrizable sets, under what conditions is the space itself metrizable? strophoid.JPG A picture of a standard curve from plane analytic geometry that will be discussed in Section III.6 of the lecture notes. ++++++++++++++++++++++++ TUESDAY, MARCH 29, 2005 ++++++++++++++++++++++++ The following file(s) was/were added: longline.pdf longline.ps Construction of a (Hausdorff) topological 1-manifold that is not metrizable. +++++++++++++++++++++++++++ WEDNESDAY, MARCH 30, 2005 +++++++++++++++++++++++++++ The following files were added: sigmacompact.doc sigmacompact.pdf sigmacompact.ps These are alternate formats for the JPG file of the same name. +++++++++++++++++++++++++++ THURSDAY, APRIL 7, 2005 +++++++++++++++++++++++++++ The following files were added: math205Cupdate1.ps math205Cupdate1.pdf Summary of the first two recommended assignments and other schedule information. solutions1.ps solutions1.pdf Solutions to the exercises in the first unit of the course homework file. +++++++++++++++++++++++++++ THURSDAY, APRIL 14, 2005 +++++++++++++++++++++++++++ The following files were added: lindiffeq.ps lindiffeq.pdf Summary of the standard solutions for (systems of) linear differential equations in terms of matrix +++++++++++++++++++++++++++ FRIDAY, APRIL 15, 2005 +++++++++++++++++++++++++++ The following files were lengthened: coursehw.ps coursehw.pdf Exercises for Unit III were added at the end. No changes were made to earlier pages. solutions2.ps solutions2.pdf Solutions to the exercises in the second unit of the course homework file. +++++++++++++++++++++++++++ WEDNESDAY, APRIL 20, 2005 +++++++++++++++++++++++++++ The following files were modified: coursehw.pdf coursehw.ps One additional problem was added to Section III.6, and there is now an addendum to Unit III with an additional exercise for Section III.4 (the notes say that a problem of the given type will be in the exercises, and the addendum makes the exercises conform to this statement). same name. +++++++++++++++++++++++++++ WEDNESDAY, APRIL 27, 2005 +++++++++++++++++++++++++++ The following files were added: solutions3A.pdf solutions3A.ps Solutions to the almost all exercises for the first sections in Unit III (thorugh III.4). takehome1.pdf takehome1.ps The first take home assignment. The following files were modified: lectnotes.pdf lectnotes.ps Typographical errors in the statement and proof of the Characterization of Direct Products on pages 83-84 were corrected, and the introduction and first section for Unit V were added. +++++++++++++++++++++++++++ WEDNESDAY, MAY 4, 2005 +++++++++++++++++++++++++++ The following files were added: exam1keyy.pdf exam1keyy.ps Answer key for the midterm examination. takehome1key.pdf takehome1key.ps Solutions for the first take home assignment. +++++++++++++++++++++++++++ FRIDAY, MAY 6, 2005 +++++++++++++++++++++++++++ The following files were added: ex1note.ps ex1note.pdf Alternate solution to the last problem of the midtern examination. th1note.ps th1note.pdf Comments on the final problem in the first take home assignment. +++++++++++++++++++++++++++ THURSDAY, MAY 12, 2005 +++++++++++++++++++++++++++ The following files were modified: lectnotes.pdf lectnotes.ps On page 117, notation was changed so that the vector addition structure map for a tangent bundle is denoted by \Sigma rather than \alpha; the reason for this change is that the use of \alpha conflicts with its frequent usage as an indexing variable for smooth coordinate charts. This is also consistent with later material in the notes, particularly on the next page. Typographical errors in the statement and proof of the Characterization of Direct Products on pages 83-84 were corrected, and the introduction and first section for Unit V were added. +++++++++++++++++++++++++++ MONDAY, MAY 16, 2005 +++++++++++++++++++++++++++ The following files were modified: lectnotes.pdf lectnotes.ps shortcontents.pdf shortcontents.ps longcontents.pdf longcontents.ps Sections V.1 and V.2 were added to the first file and some minor changes were made in Section V.A. The listings of contents were updated to incorporate the new material. +++++++++++++++++++++++++++ THURSDAY, MAY 20, 2005 +++++++++++++++++++++++++++ The following files were added: flowcurves.ps flowcurves.pdf Supplement to Unit IV with proofs of some important assertions about the integral flows of vector fields. +++++++++++++++++++++++++++ WEDNESDAY, MAY 25, 2005 +++++++++++++++++++++++++++ The following files were modified: lectnotes.pdf lectnotes.ps Now complete through the end of Section V.3 +++++++++++++++++++++++++++ FRIDAY, MAY 27, 2005 +++++++++++++++++++++++++++ The following files were modified: coursehw.pdf coursehw.ps Now complete through the end of Unit IV. extforms2005.ps extforms2005.pdf Class notes on differential forms (less expository content than the other notes). +++++++++++++++++++++++++++ THURSDAY, JUNE 2, 2005 +++++++++++++++++++++++++++ The following files were modified: math205Cupdate2.pdf math205Cupdate2.ps Information for the final examination including topics to review and suggested exercises.