**MAT 271 Foundations of Higher Mathematics****,
Section**** 01, CN 21081
Spring 201****4**

**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: sraianu@csudh.edu;
URL: http://www.csudh.edu/math/sraianu;
**

**Office hours: **Wednesday:

**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

**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 |
Saturday-Thursday |
Late Registration, Add/Drop
(fees due 48 hours after registration) |

January 20 |
Monday |
Martin Luther King Jr. Holiday-Campus
Closed, No Classes |

January 31, 12 pm |
Friday |
Instructor Drop Deadline |

February 3 |
Monday |
Summer 2014 Graduation Application Deadline |

February 6 |
Thursday |
Credit/No Credit and Audit
Grading Deadline |

February 6 |
Thursday |
Last Day to Drop from FT to PT Status with
Refund |

February 14 |
Friday |
Drop without Record of
Enrollment Deadline |

February 14 |
Friday |
Student Census |

February 15-April 17 |
Saturday-Thursday |
Serious and Compelling Reason
Required to Drop/Withdraw |

February 17 |
Monday |
President’s Day Holiday-Campus Open, No
Classes |

March 17-May 18 |
Monday-Sunday |
Spring Intersession
Registration |

March 24-July 11 |
Monday-Friday |
Summer 2014 Registration |

March 25 |
Tuesday |
Last Day for Pro-rata Refund of
Non-Resident Tuition and Tuition Fees |

March 31 |
Monday |
Cesar Chavez Holiday-Campus Closed, No
Classes |

March 31-April 5 |
Monday-Saturday |
Spring Recess (includes Cesar
Chavez Holiday)-Campus Open, No Classes |

April 16 |
Wednesday |
Summer 2014 Graduation Application Deadline
(with late fee) |

April 18-May 8 |
Friday-Thursday |
Serious Accident/Illness
Required to Drop/Withdraw |