Although this requirement is stated in the catalogue as "Mathematics 340L or 341," the requirement really is M 341. However, M340L will be counted in place of M341 for students switching from another major who have already taken M340L and for students who have transferred from another school with transfer credit for M 340L.

Linear algebra is the study of vectors, matrices, and related topics. It has applications to many areas and is used in many other branches of mathematics.

Although the courses have considerable overlap, there are some important differences:

• M341 is taught in small classes, whereas M340L is taught in large lecture sections
• M341 includes more proofs than M340L. To compensate, M341 covers fewer topics than M340L.
• M341 is restricted to math majors; M340L is open to students in other majors

M 341 gives experience with proofs that helps prepare students for the later algebra and analysis courses. Students transferring from other majors or other colleges who have credit for M 340L will need to gain this experience with proofs elsewhere.

 M341 (but not M340L) is a proof course, and therefore helps address the Logical Reasoning portion of SBEC Standard V: Mathematical Processes:

 "The beginning teacher of mathematics is able to:

• (5.1s) apply correct mathematical reasoning to derive valid conclusions from a set of premises;
• (5.2s) apply principles of inductive reasoning to make conjectures and use deductive methods to evaluate the validity of conjectures;
• (5..3s) use formal and informal reasoning to explore, investigate, and justify mathematical ideas;
• (5.4s) recognize examples of fallacious reasoning;
• (5.5s) evaluate mathematical arguments and proofs; and
• (5.6s) provide convincing arguments or proofs for mathematical theorems."

 Both courses also address these items of the Connections and Communication portions of Standard V:

• "(5.16s) recognize and use multiple representations of a mathematical concept
• (5.17s) apply mathematical methods to analyze practical situations; and
• (5.18s) use mathematics to model and solve problems in other disciplines …
• (5.21s) translate mathematical statements among developmentally appropriate language, standard English, mathematical language, and symbolic mathematics; …
• (5.24s) use the language of mathematics as a precise means of expressing mathematical ideas."

Both courses also address the following items of Standard II: Patterns and Algebra:

• "(2.11s) use a variety of representations and methods … to solve linear … systems;…
• (2.29s) represent and solve problems using techniques of linear and matrix algebra;
• (2.30s) apply the properties of vectors and vector algebra to solve pure and applied problems;
• (2.31s) demonstrate an understanding of algebraic structures (e.g. … vector spaces) …"

Some sections of these courses may also address the following portion of Standard III: Geometry and Measurement:

• "(3.24s) relate geometry to algebra by representing transformations as matrices and use this relationship to solve problems."

These courses (especially M 341) help prepare you to teach according to the following Basic Understandings for Algebra II:

• (2) Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways to represent mathematical situations and to express generalizations. Students study algebraic concepts and the relationships among them to better understand the structure of algebra.
• (3) Functions, equations, and their relationship. The study of functions, equations, and their relationship is central to all of mathematics. Students perceive functions and equations as means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations.
• (4) Relationship between equations and functions. Equations arise as a way of asking and answering questions involving functional relationships.
• (6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling, and justification and proof.

M341 also helps prepare the teacher to teach according to Geometry Knowledge and Skills (b.3): The student understands the importance of logical reasoning, justification, and proof in mathematics. In particular, M 341 involves the following specific skill in this section: The student

• (A) determines if the converse of a conditional statement is true or false;
• (C) demonstrates what it means to prove mathematically that statements are true;
• (D) uses inductive reasoning to formulate a conjecture; and
• (E) uses deductive reasoning to prove a statement.

How do these courses relate to the National Council of Teachers of Mathematics' Principles and Standards for School Mathematics?

 These courses can help you develop your skills in reasoning and proof so that you can teach according to the 9-12 Standard for Reasoning and Proof. In addition, they will help give you the background in working with matrices in order to represent transformations by matrices, as specified in the Geometry Standard for Grades 9 - 12.

 How do these courses relate to other courses I might be taking?

• M 325K (Discrete Mathematics) lays a foundation in areas such as logic, basic proof techniques, and mathematical induction that are built upon in these courses.
• M 360M (Mathematics as Problem Solving) helps develop problem solving and proof techniques that are useful in these courses.
• M 341 is a prerequisite for M 343K and M 373K, two of your three choices for the Algebra requirement
• M 341 is a prerequisite for both of your choices, M 361K and M365C, for the Analysis requirement.

• Unless you have a strong background in proof, be sure to take M 325K before M 341.
• Keep in mind the SBEC Logical Reasoning standards quoted above. Focus on developing them in this course, so that you can apply them to other areas of mathematics as well as linear algebra.
• Many students find M 341 challenging, so be prepared for a challenge. Don't expect the ideas to come automatically; you will need to work at them. Be sure to devote adequate time to studying. This usually means more than just doing homework and studying for exams.