MAT 271 Foundations of Higher Mathematics,  Section 01, CN 21081 Spring 2014


Class meets MW 7:00 PM – 8:15 PM in SCC 1304.

Instructor:  Serban Raianu

Office: NSM A-123; Office phone number: (310) 243- 3139

e-mail address:; URL:;

Office hours:  Wednesday: 2:20 PM - 2:50 PM, 4:00 PM - 5:00 PM, Friday: 2:30 PM - 5:00 PM, or by appointment.


Course Description: MAT 271 Foundations of Higher Mathematics, prepares students for the transition from lower division mathematics courses - which are often based on computation - to upper division mathematics courses - which typically are based on proof. Mathematical rigor, proof strategies, and writing are emphasized. Covers elementary mathematical logic, including propositional and predicate calculus, set theory, equivalence and order relations


Text: Frédéric Brulois, Lecture Notes on the Foundations of Higher Mathematics, Spring 2010. The Lecture Notes will be available free on Blackboard.


Objectives: After completing MAT 153 the student should be able to:

critique a purported proof,

use a variety of proof strategies in proving propositions, including direct proof, proof by contraposition, proof by

contradiction, proof by exhaustion, proof by induction,

devise existence proofs, either constructive or using other existential proposition,

prove economically that two or more statements are equivalent,

write proofs that are logically coherent, written in grammatically correct English, using standard mathematical ideas

in undergraduate mathematics courses and textbooks

understand the concept of, and construct counter-examples to, false statements,

produce truth tables for statements in the propositional calculus,

negate compound and quantified propositions,

use reliably the concepts of elementary set theory, including set notation, set operations, inclusion, subsets, power sets,

indexed families of sets and their union and intersection, Cartesian product, binary relations including equivalence and

order relations, partitions and their connection to equivalence relations, simple and directed graphs, equivalent sets,

cardinals, finite sets, countable sets,

operate in a formal and rigorous way with the concept of function and related concepts, including composition of

functions, inverse of a function, restriction of a function, injections, surjections, and bijections, induced set functions,

and, throughout, and

use standard mathematical notation and terminology and avoid nonsensical expressions and statements.


Prerequisites: MAT 191 or equivalent with a grade of "C" or better.


Grades: Grades will be based on three in‑class 70-minutes examinations (60% total), a comprehensive final examination (25%), and quizzes, homework, attendance and other assignments (15%) for the remainder.

The exact grading system for your section is the following:

Each of the three 70-minutes exams will be graded  on a 100 scale, then the sum of the scores is divided by 5 and denoted by E.

Homework will be due every Monday. Each weekly homework assignment is worth up to 5 points. The homework assignments will be posted on Blackboard. No late homework will be accepted. The average of all homework scores is denoted by H.


It is important to do the homework, because problems on the quizzes and exams will be similar to the problems in the homework assignments.


5 to 10 minutes quizzes will be given in principle every Monday, and will be graded on a scale from 1 to 5. The average of the quizzes scores is denoted by Q.

There are also 5 points awarded for attendance and class participation. This portion of the grade is denoted by A.

The final exam will be graded out of a maximum possible 200, then the score is divided by 8 and denoted by F. 

To determine your final grade,  compute E+H+Q+A+F. The maximum is 100, and the grade will be given by the rule:

         A: 93‑100;      A‑: 90‑92;      B+: 87‑89;      B: 83‑86;   B‑: 80‑82

        C+: 77‑79;      C: 73‑76;        C‑: 70‑72;      D+: 67‑69;   D: 60‑66;     F: Less than 60.


Makeups: No makeup examinations or quizzes will be given. If you must miss an examination for a legitimate reason, discuss this, in advance, with me, and I may then substitute the relevant score from your final examination for the missing grade.


Accomodations for Students with Disabilities: Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH B250. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.


Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)


Exam rules: Students must leave their CSUDH student ID on their desk for the duration of the exam. Cell phones, iPhones, iPods, or PDAs of any kind, as well as headphones, may not be used at all during a test. Students are discouraged from leaving the exam room during the period of the exam. Restroom breaks must be kept under five minutes and are limited to one/exam. You will be penalized 5 points if you are gone more than five minutes.  No more than one student can be out of the room at any given time during an exam. If a student finds it necessary to leave the room under these circumstances, they are not permitted to access computer terminals, smoke, read notes/books, or talk with others. If a student is found engaging in this behavior, appropriate disciplinary action will be taken.  Whenever a student leaves the room, they must turn their exam upside down on their desk. All book bags or similar items will be deposited in the front of the class for the duration of the test.



Tentative schedule


M 1/20: Martin Luther King Jr. Holiday

W 1/22: 1.1 Logical connectives

M 1/27: 1.2 Conditionals and biconditionals

W 1/29: 1.3 Complete collections of logical connectives

M 2/3: 1.4 Introduction to set theory

W 2/5: 1.5 Quantifiers

M 2/10: 1.6 Predicates

W 2/12: 2.1 Proof methods 1 through 6

M 2/17: Presidents’ Day Holiday

W 2/19: 2.2 Proof methods 7 through 10: conditionals

M 2/24: Review

W 2/26: Exam I

M 3/3: 2.3 Proof methods 11 through 21: quantified statements

W 3/5: 2.4 Proof method 22: Principle of Mathematical Induction

M 3/10: 2.5 Proof method 23: Principle of Strong Induction

W 3/12: 3.1 Basic notions of set theory

M 3/17: 3.2 Set operations

W 3/19: 3.3 Indexed families of sets

M 3/24: 3.4 Cartesian products

W 3/26: Review

M 3/31: Spring Recess

W 4/2: Spring Recess

M 4/7: Exam II

W 4/9: 4.1 Relations

M 4/14: 4.2 Operations on relations

W 4/16: 4.3 Properties of relations

M 4/21: 4.4 Equivalence relations

W 4/23: 4.5 Partitions

M 4/28: 4.6 Order relations

W 4/30: 4.7 Well orderings

M 5/5: Review

W 5/7: Exam III

F 5/9: Review



Final examination: Monday, May 12, 7:00 PM - 9:00 PM.


Important dates


January 18-February 6


Late Registration, Add/Drop (fees due 48 hours after registration)

January 20


Martin Luther King Jr. Holiday-Campus Closed, No Classes

January 31, 12 pm


Instructor Drop Deadline

February 3


Summer 2014 Graduation Application Deadline

February 6


Credit/No Credit and Audit Grading Deadline

February 6


Last Day to Drop from FT to PT Status with Refund

February 14


Drop without Record of Enrollment Deadline

February 14


Student Census

February 15-April 17


Serious and Compelling Reason Required to Drop/Withdraw

February 17


President’s Day Holiday-Campus Open, No Classes

March 17-May 18


Spring Intersession Registration

March 24-July 11


Summer 2014 Registration

March 25


Last Day for Pro-rata Refund of Non-Resident Tuition and Tuition Fees

March 31


Cesar Chavez Holiday-Campus Closed, No Classes

March 31-April 5


Spring Recess (includes Cesar Chavez Holiday)-Campus Open, No Classes

April 16


Summer 2014 Graduation Application Deadline (with late fee)

April 18-May 8


Serious Accident/Illness Required to Drop/Withdraw