Math 4130/5130: Linear Algebra, Fall 2021

Exams and Homework

1. Tips for Reading Your Mathematics Textbook
2. Expectations of Higher Level Math Courses
3. First Experiences with Writing Proofs

• Syllabus
• Information Sheet (Due Wednesday, August 25)

Miscellaneous Resources

• The history of mathematics is an important subject. It gives a context in which to view the results that one learns in math classes. Furthermore it shows that mathematics is, first and foremost, a human activity. In the historical development of Linear Algebra, we see that the concept of a vector dates back as early as the work of Bolzano in the beginning of the 19th century. Initially vectors were used in the study of geometry, giving a way to "coordinatize" space. Transformations on space often took the form of matrices, and this prompted the study of such matrix properties as determinants and canonical forms. Later, in the work of Poncelet and Chasles, a move was made to a coordinate-free, or synthetic, geometry. This was the beginning of the notion of an abstract vector space, in which one replaces concrete spaces by abstract spaces satisfying certain axioms, and in which matrices are replaced by linear operators on these spaces. Today the influence of Linear Algebra extends far beyond geometry, and the concept of an (abstract) vector space arises in a variety of contexts. Consequently, Linear Algebra has had applications to numerous areas of mathematics as well as many areas of physics.
  
  Here you can find out more about:
  

  • The History of Abstract Vector Spaces (also called Linear Spaces),
  • The History of Matrices and Determinants, and
  • Other Topics in the History of Mathematics.

  
  
  
• The Wikipedia entry on Linear Algebra.
  
  
• Some Linear Algebra Tools on the web.
  
  
• Also check out some unsolved problems in mathematics:
  
  • Famous Unsolved Problems in Mathematics
  • A List of Mathematical Conjectures
  • The Millennium Prize Problems, each of which carries an award of $1,000,000 to anyone who can solve the problem.
  
  and the various awards that are given to people working towards the solutions of these, and many other, problems in mathematics:
  
  • The Fields Medal, often called the Nobel Prize of mathematics
  • The Abel Prize, established in 2001.