MATH 1312 - Introduction to Mathematical Reasoning - University of Houston

# MATH 1312 - Introduction to Mathematical Reasoning

***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

Prerequisites: A satisfactory score on a placement examination. *Note: May not apply toward a degree from the College of Natural Sciences and Mathematics.

Textbook: Elementary Geometry for College Students, Daniel C. Alexander and Geralyn M. Koeberlein, 6th edition, Houghton Mifflin Company, 2015, 2011: (Summer 2019: 6 TH ED. ISBN: 9781285195698) (Fall 2019 & thereafter: 7 TH ED. ISBN: 9781337614085)

Course Description:  Credit 3 hours (3-0). Principles of logic and proof, set theory, formal and informal geometry.

Supplies: A small ruler and compass will be needed for some sections and a calculator will be needed for most sections.

*Note: The information contained in this class outline is an abbreviated description of the course. Additional important information is contained in the Departmental Course Policies statement and at your instructor’s personal webpage. You are responsible for knowing all of this information.

Syllabus:

Chapter 1 —Foundations of Geometry

1.1 Inductive and Deductive Reasoning
1.2 Points, Lines, and Planes
1.3 Segments, Rays, and Angles
1.4 Introduction to Deductive Proofs
1.5 Formalizing Geometric Proofs
1.6 Relationships: Parallel and Perpendicular Lines
1.7 Formal Proofs of Theorems

Chapter 2 — Triangles

2.1 Classifying Triangles
2.2 Congruent Triangles
2.3 Proofs Involving Congruence
2.4 Isosceles Triangles, Medians, Altitudes, and Concurrent Lines
2.5 Proving Right Triangles Congruent
2.6 Constructions Involving Triangles

Chapter 3 —Parallel Lines and Polygons

3.1 Indirect Proof and the Parallel Postulate
3.2 Transversals and Angles
3.3 Polygons and Angles
3.5 Define and Use Triangle Inequality Theorems

4.1 Parallelograms
4.2 Rhombus and Kite
4.3 Rectangles and Squares
4.4 Trapezoids

Chapter 5 — Similar Polygons and the Pythagorean Theorem

5.1 Ratio and Proportion
5.2 Similar Polygons
5.3 Properties of Right Triangles
5.4 Pythagorean Theorem
5.5 Inequalities Involving Triangles
5.6 Segments Divided Proportionally in Triangles

Chapter 6 — Circles

6.1 Circles and Related Segments and Angles
6.2 More Angle measures in a Circle
6.3 Line and Segment Relationships in the Circle
6.6 Concurrence of Lines

Chapter 7 — Area of Polygons and Circles

7.1 Area and Initial Postulates
7.2 Perimeter and Area of Polygons
7.3 Regular Polygons and Area

Chapter 8 — Solid Geometry

8.1 Planes and Polyhedrons
8.2 Prisms
8.3 Pyramids
8.4 Cylinders and Cones and Spheres

Homework:

Section Exercises
1.1 #3, 4, 13, 15, 17, 25, 27, 29, 33, 34, 39, 41, 43, 55
1.2 #3-7, 9, 11-15, 19, 21, 24, 35-39, 41-43, 46
1.3 #1-6, 11, 14-17, 25, 29, 31
1.4 #1, 3, 5-8, 10-13, 15, 17, 19, 21, 25, 31, 34
1.5 #7-10, 11, 14, 15, 17, 25, 29
1.6 #1, 3, 5, 8, 9, 11
1.7 #9-15, 17, 21

 2.1 #1-4, 9, 15, 19 2.2 #1, 3, 5, 9, 13, 17 2.3 #1, 3, 5, 7, 9, 11, 17, 23, 25 2.4 #1, 3, 5, 7, 9, 11, 13, 19, 23, 31, 33, 38-40 2.5 #3-25 odd, 31, 35 2.6 #5, 7, 13, 23, 29

 3.1 #1, 8-19, 21, 25, 27, 31 3.2 #1, 3, 5, 11, 17, 19, 27 3.3 #5, 7, 9, 11, 15, 17, 19, 21, 23, 29, 33 3.5 #1, 2, 3, 11, 15, 17, 19, 21, 25

 4.1 #3, 5, 7, 9, 17, 21, 25 4.2 #1, 7, 9, 11, 19, 25, 29 4.3 #1, 3, 5, 9, 13, 17, 27 4.4 #11, 13, 15, 25

 5.1 #5, 7, 9 ,15 , 17, 21, 29 5.2 #1, 9, 13, 15, 17, 21, 29 5.3 #5, 7, 9, 11, 17 5.4 #7, 9, 13, 15, 17, 21, 27 5.5 #1, 3, 5, 7, 9, 13, 20 5.6 #5,7, 9, 13, 17

 6.1 #1, 3, 5, 9, 13, 19 6.2 #1,3, 7, 15 6.3 #1,3, 7, 15, 19 6.6 #1-7, 11, 17, 27

 7.1 #1, 9, 11, 13, 17, 19, 27 7.2 #1, 5, 9, 13, 15, 33 7.3 #9, 13, 15, 17, 19, 25

 8.1 #1, 5, 7, 9, 15 8.2 #5, 7, 9, 11, 21 8.3 #3, 5, 7, 13, 15, 21 8.4 #7, 23, 29

CSD Accommodations:

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or online version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.

UH CAPS

Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.