==Syllabus==
''The simplicity of nature is not to be measured by that of our conceptions.'' 
''Infinitely varied in its effects, nature is simple only in its causes, 
''and its economy consists in producing a great number of phenomena,'' 
''often very complicated, by means of a small number of general laws.'' 
[https://en.wikipedia.org/wiki/Pierre-Simon_Laplace Pierre-Simon Laplace (1749-1827)]

* '''Time and Place.''' MW 13:30-14:50 in TWH 313.

* '''Instructor.''' Helmut Knaust, Bell Hall 219, [mailto:hknaust@utep.edu hknaust@utep.edu], 747-7002

* '''Office Hours.''' M 15:00-16:00, TR 16:30-17:30, or by appointment.

* '''Teaching Assistant.''' Mr. Edward Laryea. Office Hours: T 13:30-15:30, R 13:30-14:30 in MaRCS.

* '''Other Sources of Help.''' Visit the [https://www.utep.edu/science/math/marcs/ MaRCS Tutoring Center] in the Library.

* [[image:BDH.jpg|150px|right]]'''Textbook. ''' Paul Blanchard, Robert L. Devaney, Glen R. Hall. ''Differential Equations.'' [https://www.cengage.com/c/differential-equations-with-de-tools-printed-access-card-4e-blanchard-devaney-hall/9781133109037/ Cengage Learning , 4th edition.] The parts of the textbook covered in class are intended to be read in advance.

* '''Prerequisites.''' I will assume that you have a thorough knowledge of the material covered in your Precalculus and your first two Calculus courses. In particular, it is essential that you are comfortable with techniques of integration and the method of partial fractions.

* '''Course Contents.''' The course will cover the following material:
** Chapter 1.1-1.9 (4 weeks)
** Chapter 2.1-2.6 (2.5 weeks)
** Chapter 3.1-3.7 (4 weeks)
** Chapter 5.1-5.2 (1.5 weeks)
** Chapter 6.1-6.4 incl. selected topics from Chapter 4 (2.5 weeks)

* '''Course Objectives.''' During the course you should expect (and I will expect) that you make considerable progress in the following areas:

# Apply standard techniques to analyze and solve ordinary differential equations: using analytical, numerical and qualitative methods; using the method of the Laplace transform.
# Be able to model with differential equations and interpret the results of their mathematical analysis.
# Understand the fundamental difference between linear and non-linear differential equations.

* '''Homework.''' I will regularly assign homework. Your homework will not be graded. Homework assignments will also include reading assignments.

* '''Quizzes. ''' There will be unannounced quizzes on a regular basis. Quiz problems will be identical to previously assigned homework problems. The quizzes will contribute 10% to your grade.

* '''Tests.''' Exams will be given on the following Wednesdays: '''February 18''', '''March 25''', and '''April 22'''. Each exam counts 20% of your grade.

* '''Make-up Exams.''' Make-up tests will only be given under extraordinary circumstances, and only if you notify the instructor '''prior''' to the exam date. There will be no make-up quizzes. Your worst quiz grade will be dropped.

* '''Final exam.''' The final on '''Wednesday, May 13, 16:00-18:45''' is mandatory and comprehensive. It counts 30% of your grade.

* '''Grades.''' Your grade will be based on the percentage of the total points that you earn during the semester. You need at least 90% of the points to earn an A, at least 80% for a B, at least 70% for a C, and at least 60 % for a D.

* '''Calculators.''' You may use a '''non-graphing''' calculator (not a cell phone, etc.) during tests and the final. If you have doubts about whether your calculator qualifies, ask me '''before''' the first test.

* '''Mathematica.''' I will show in class and make available a few ''Mathematica'' notebooks. ''Mathematica'' is available at https://www.utep.edu/technologysupport/ServiceCatalog/SOFTWARE_PAGES/soft_mathematica.html. Choose "Mathematica Online", not "Mathematica"! I do not expect you to learn how to code, but if you want to learn more about writing ''Mathematica'' code, a nice but voluminous introduction to Mathematica can be found at [https://www.wolfram.com/language/elementary-introduction/ An Elementary Introduction to the Wolfram Language, by Stephen Wolfram].

* '''Time Requirement.''' I expect that you spend an absolute minimum of six hours a week outside of class on reading the textbook, reviewing your class notes, completing homework assignments, and preparing for the next class. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.

* '''Drop Policy.''' The class schedule lists '''Thursday, April 2''', as the last day to drop with an automatic "W". After the deadline, I can only drop you from the course with a grade of "F".

* '''Attendance.''' You are strongly encouraged to attend class every day. I expect you to arrive for class on time and to remain seated until the class is dismissed. Students with six or more absences (excused or unexcused) will be dropped from the course with a grade of "F".

* '''Academic Integrity.''' All students must abide by UTEP's academic integrity policies. For detailed information visit the [https://www.utep.edu/student-affairs/standards/ Office of Community Standards] (OCS) website. Academic Integrity is a commitment to fundamental values. Specifically, these values are defined as follows:
** Honesty: advances the quest for truth and knowledge by requiring intellectual and personal honesty in learning, teaching, research, and service.
** Trust: fosters a climate of mutual trust, encourages the free exchange of ideas, and enables all to reach their highest potential.
** Fairness: establishes clear standards, practices, and procedures and expects fairness in the interaction of students, faculty, and administrators.
** Respect: recognizes the participatory nature of the learning process and honors and respects a wide range of opinions and ideas.
** Responsibility: upholds personal responsibility and depends upon action in the face of wrongdoing.

* '''AI (Artificial Intelligence) Use.''' Use of AI technologies or automated tools, particularly generative AI such as ChatGPT, Claude, Gemini, or DALL-E, is only allowed with approval from the instructor '''before''' being used. Without permission, you will be expected to think creatively and critically to complete assignments without aid from these tools. If given permission to use any of these tools, students must properly cite and give full credit to the program used upon submission of the assignment.

* '''Military Service.''' If you are a military student with the potential of being called to military service and/or training during the course of the semester, please contact the instructor as soon as possible.

* '''Counseling Center.''' You are encouraged to go to Counseling and Psychological Services (202 Union West) for personal assistance as you work through personal concerns. Confidential counseling services are offered in English or in Spanish. Phone: 747-5302.

* '''Disabilities.''' If you have a disability and need special accommodation, please contact the [https://www.utep.edu/student-affairs/cass/ Center for Accommodations and Support Services] (CASS). The Center aspires to provide students accommodations and support services to help them pursue their academic, graduation, and career goals. Phone 747-5148. E-mail: cass@utep.edu.

===Classnotes===
[http://helmut.knaust.info/class/202620_2326/Notes/0408.pdf April 8] [http://helmut.knaust.info/class/202620_2326/Notes/0406.pdf April 6] | [http://helmut.knaust.info/class/202620_2326/Notes/0401.pdf April 1] | [http://helmut.knaust.info/class/202620_2326/Notes/0330.pdf March 30] | [http://helmut.knaust.info/class/202620_2326/Notes/0323.pdf March 23] | [http://helmut.knaust.info/class/202620_2326/Notes/0311.pdf March 11] | [http://helmut.knaust.info/class/202620_2326/Notes/0309.pdf March 9] | [http://helmut.knaust.info/class/202620_2326/Notes/0304.pdf March 4] | [http://helmut.knaust.info/class/202620_2326/Notes/0302.pdf March 2] | [http://helmut.knaust.info/class/202620_2326/Notes/0216.pdf February 16] | [http://helmut.knaust.info/class/202620_2326/Notes/0211.pdf February 11] | [http://helmut.knaust.info/class/202620_2326/Notes/0209.pdf February 9] | [http://helmut.knaust.info/class/202620_2326/Notes/0204.pdf February 4] | [http://helmut.knaust.info/class/202620_2326/Notes/0202.pdf February 2] | [http://helmut.knaust.info/class/202620_2326/Notes/0128.pdf January 28] | [http://helmut.knaust.info/class/202620_2326/Notes/0126.pdf January 26] | [http://helmut.knaust.info/class/202620_2326/Notes/0121.pdf January 21]

===Materials===
[https://www.wolframcloud.com/env/hknaust/2326/TDPlane.cdf TD Plane] | [https://www.wolframcloud.com/env/hknaust/2326/Spring2.cdf Damped Spring] |
[http://helmut.knaust.info/class/202620_2326/FlightOfAGlider.cdf Flight of a Glider (''Mathematica'' demonstration)] |
[http://helmut.knaust.info/class/202310_2326/WS02.pdf Worksheet 2 (glider)] | [http://helmut.knaust.info/class/201620_2326/Hilbert16.pdf Hilbert's 16th Problem] | [https://www.tandfonline.com/doi/pdf/10.4169/math.mag.86.3.204 Cooling Coffee Without Solving Differential Equations], by Robert Israel, Peter Saltzman and Stan Wagon (''Math. Mag.'' '''86''' (2013), pp.204–210) | [http://helmut.knaust.info/class/202620_2326/DEQ.nb DEQ.nb (''Mathematica'' notebook)] | [http://helmut.knaust.info/class/202620_2326/grill.png Grill snapshot] | [https://homepages.bluffton.edu/~nesterd/apps/slopefields.html Slope field and phase plane plotter], by Darryl Nester | [https://demonstrations.wolfram.com/BungeeJumping/ Bungee jump (''Mathematica'' demonstration)] | [http://helmut.knaust.info/class/202620_2326/WS01.pdf Worksheet 1 (bungee jump)]

===Homework===
* 4/6: Read 3.7,5.1. Problems: 3.7: 4,10
* 4/1: Read 3.5-3.7. Problems: 3.5: 3,4,18; 3.6: 8,10,12,32
*3/30: Read 3.3-3.4. Problems: 3.3: 14,19; 3.4: 4,6,16,22,23
* 3/16: Read 3.2. Problems: 3.2: 2,6,8,14,19;
* 3/9 Read 3.1-3.2. Problems: 3.1: 5,16,19,26,34
* 3/4: Read 2.5-2.6; 3.1-3.2. Problems: 2.5: 5,7 (<math>\Delta t=0.5,0.25</math>); 2.6: 3,4
*3/2: Read 2.2, 2.4-2.6. Problems 2.1: 8ab; 2.2: 9,11,14,16; 2.4: 5,6,7
*2/25: Read 2.1-2.2. Problems 2.1: 1-6
*2/11: Read 1.7. Problems: 1.7: 2,4,6,16
*2/9: Read 1.6,1.7. Problems 1.6: 2,12,30,36
*2/4: Read 1.4-1.6. Problems: 1.4: 2,6; 1.5: 2,11
*2/2: Read 1.3-1.5 HW Problems: 1.9: 24,25. 1.3: 10,13,14,16
*1/28: Read 1.3,1.4. HW Problems: 1.2: 6,10,22,36,40,41
*1/26: Read 1.2,1.9. HW Problems: 1.2: 1,2; 1.9:1,4,6,10
*1/21: Read 1.2,1.9.

[[File:plotDF.jpg|600px|frame|caption]]

File:PlotDF.jpg

2026-04-08T21:15:59Z

HelmutKnaust: HelmutKnaust uploaded a new version of "File:PlotDF.jpg"

2026-03-31T22:50:58Z

HelmutKnaust: /* Open Problems */

==Syllabus for Math 4303==
''The greatest danger for most of us is not'' 
''that our aim is too high and we miss it,'' 
''but that it is too low and we reach it. ''
(Michelangelo Buonarroti)
* '''Time and Place.''' TR 15:00-16:20, CRBL C201.
__NOTOC__
* '''Instructor.''' Dr. Helmut Knaust, Bell Hall 219, [mailto:hknaust@utep.edu hknaust@utep.edu], (915) 747-7002

* '''Office Hours.''' M 15:00-16:00, TR 16:30-17:30, or by appointment.

* [[image:MfHST.jpg|right]]'''Textbook. ''' Zalman Usiskin, Anthony L. Peressini, Elena Marchisotto, and Dick Stanley. ''Mathematics for High School Teachers - An Advanced Perspective.'' Prentice Hall. ISBN-13 978-0130449412 (paperback). '''A PDF version of the textbook is available at https://knowledge.uchicago.edu/record/5793.''' The textbook is required at all class meetings, and the parts covered in class are intended to be read in full.

* '''Course Requirements.'''
** ''Quizzes, etc.(15%)'': I will give regular, but unannounced quizzes in class. Quiz problems will be identical to prior homework assignments. There will also be some other assignments (worksheets, writing assignments). Your worst two grades will be dropped.
** ''Exams (25% total)'': You will have two in-class exams on the following days: '''Tuesday, March 3''' and '''Thursday, April 30'''.
** ''Class Presentations (25%)'': Student pairs will each design and conduct all classroom activities for a class session and will be responsible for the content covered in that session. Each group will also create homework assignments.
*** The groups will meet with me two weeks before their presentation for a ''trial run'' so that I will know that you are prepared. This is not optional. If you do not meet with me, you will lose half of your possible points.
** ''Final Project (20%)'': There are mathematics problems that require more attention than just one day. Some of these problems are, for example, found at the end of the chapters in the textbook. Student groups will complete such a problem and present the results in class during the final period '''Thursday, May 14 at 16:00 – 18:45.'''
** ''Class Participation (15%)'': This is a Mathematics class, and, as you know, Mathematics is not a spectator sport. During class I expect you to participate. This is an active class where students daily present solutions to their peers. The participation grade will be based both on the quality and frequency of your contributions.
* '''Grades.''' Your grade will be based on the percentage of the total points that you earn during the semester. You need at least 90% of the points to earn an A, at least 80% for a B, at least 70% for a C, and at least 60 % for a D.

* '''Make-up Exams'''. Make-up tests will only be given under extraordinary circumstances, and only if you notify the instructor prior to the exam date. There will be no make-up quizzes.

* '''Time Requirement.''' I expect that you spend an absolute minimum of six hours a week outside of class on preparing your group activities, reading the textbook, preparing for the next class, reviewing your class notes, and completing homework assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.

* '''Attendance.''' Due to the nature of the course you are strongly encouraged to attend class every day. I expect you to arrive for class on time and to remain seated until the class is dismissed. Students with six or more absences (excused or unexcused) will be dropped from the course with a grade of "F".

* '''Mathematica.''' I will show in class and make available a few ''Mathematica'' notebooks. ''Mathematica'' is available at https://www.utep.edu/technologysupport/ServiceCatalog/SOFTWARE_PAGES/soft_mathematica.html. Choose "Mathematica Online", not "Mathematica"! I do not expect you to learn how to code, but if you want to learn more about writing ''Mathematica'' code, a nice but voluminous introduction to Mathematica can be found at [https://www.wolfram.com/language/elementary-introduction/ An Elementary Introduction to the Wolfram Language, by Stephen Wolfram].

* '''Drop Policy.''' The class schedule lists '''Thursday, April 2''', as the last day to drop with an automatic "W". After the deadline, I can only drop you from the course with a grade of "F".

* [https://capitol.texas.gov/tlodocs/89R/billtext/pdf/SB00037F.pdf Texas Senate Bill 37]. The 2025 law reshaping the governance of public colleges and universities, does not prohibit the teaching of any particular content in academic courses at public colleges and universities in Texas. Although earlier versions of the bill included censorship of specific course content, these provisions were removed in the final version. Expectations and academic freedom for teaching and class discussion have not been altered due to prohibitions in SB 37, and students should not feel the need to censor their speech pertaining to topics including race, gender, gender identity, ethnicity, politics, society, and religion.

* '''Academic Integrity.''' All students must abide by UTEP's academic integrity policies. For detailed information visit the Office of Student Conduct and Conflict Resolution (OSCCR) website. Academic Integrity is a commitment to fundamental values. From these values flow principles of behavior that enable academic communities to translate ideals into action.” Specifically, these values are defined as follows:
** Honesty: advances the quest for truth and knowledge by requiring intellectual and personal honesty in learning, teaching, research, and service.
** Trust: fosters a climate of mutual trust, encourages the free exchange of ideas, and enables all to reach their highest potential.
** Fairness: establishes clear standards, practices, and procedures and expects fairness in the interaction of students, faculty, and administrators.
** Respect: recognizes the participatory nature of the learning process and honors and respects a wide range of opinions and ideas.
** Responsibility: upholds personal responsibility and depends upon action in the face of wrongdoing.

* '''AI (Artificial Intelligence) Use.''' Use of AI technologies or automated tools, particularly generative AI such as ChatGPT or DALL-E, is only allowed with approval from the instructor '''before''' being used. Without permission, you will be expected to think creatively and critically to complete assignments without aid from these tools. If given permission to use any of these tools, students must properly cite and give full credit to the program used upon submission of the assignment.

* '''Military Service.''' If you are a military student with the potential of being called to military service and/or training during the course of the semester, contact the instructor as soon as possible.

* '''Counseling Center.''' You are encouraged to go to [https://www.utep.edu/student-affairs/counsel/ Counseling and Psychological Services] (202 Union West) for personal assistance as you work through personal concerns. Confidential counseling services are offered in English or in Spanish. The Center provides a Crisis Hotline at 747-5302.

* '''Disabilities.''' If you have a disability and need special accommodation, please contact the [https://www.utep.edu/student-affairs/cass/ Center for Accommodations and Support Services] (CASS). The Center aspires to provide students with accommodations and support services to help them pursue their academic, graduation, and career goals. Phone 747-5148. E-mail: cass@utep.edu.

==Final Presentations==
[http:///helmut.knaust.info/class/202620_4303/FProjects2026.pdf Final Projects] | [http://helmut.knaust.info/BD/Gallian.pdf Advice on Giving a Good PowerPoint Presentation], by Joseph Gallian. | [http://helmut.knaust.info/presentations/2008/20081018_GEPCTM/Mersenne.pdf A sample project: Mersenne Primes.]

==Lesson Presentations==
[http:///helmut.knaust.info/class/202620_4303/Pres.pdf Presentation Details and Assignments] | [http:///helmut.knaust.info/class/202620_4303/PresRubric.pdf Rubric for Presentations]

==Open Problems==
*3.1.1: 2ab,3bcd,6,8.
* '''I2''' Let G be the set of all isometries with a fixed point <math>z^*</math>, i.e., <math>G=\{f:\C\to \C\ | \ F \mbox{ is an isometry and } f(z^*)=z^*\}</math>. Show that G forms a group with the binary operation of composition.
* '''I3''' Let H be the set of all isometries <math>f:\mathbb{C}\to \mathbb{C}</math> of the form <math>f(z)=z_0+ z e^{i\theta}</math> for some <math>z_0\in\C</math> and <math>\theta \in \R</math>. Is H a group with the binary operation of composition?
* '''I4''' Let K be the set of all isometries <math>f:\mathbb{C}\to \mathbb{C}</math> of the form <math>f(z)=z_0+ \overline{z} e^{i\theta}</math> for some <math>z_0\in\C</math> and <math>\theta\in\R</math>. Is K a group with the binary operation of composition?
* 2.2.2: 6,7

==Homework==
*3/31 '''Lesson 1 (4/2)''': 4.1.1: 1, 4a,7a; 4.1.2: 1a,2b,3
*3/26: Read 3.1.1-3.1.2. Problems 3.1.1: 2abc,3bcd,6,8.
*3/12: (1) Let <math>f(z)=z_0+ z e^{i\alpha}</math> and <math>g(z)=z_1+ \overline{z} e^{i\beta}</math>. Compute their compositions <math>f\circ g</math> and <math>g\circ f</math>. (2) Let G be the set of all isometries with a fixed point <math>z^*</math>, i.e., <math>G=\{f:\C\to \C\ | \ F \mbox{ is an isometry and } f(z^*)=z^*\}</math>. Show that G forms a group with the binary operation of composition. (3) Let H be the set of all isometries <math>f:\mathbb{C}\to \mathbb{C}</math> of the form <math>f(z)=z_0+ z e^{i\theta}</math> for some <math>z_0\in\C</math> and <math>\theta \in \R</math>. Is H a group with the binary operation of composition? (4) Let K be the set of all isometries <math>f:\mathbb{C}\to \mathbb{C}</math> of the form <math>f(z)=z_0+ \overline{z} e^{i\theta}</math> for some <math>z_0\in\C</math> and <math>\theta\in\R</math>. Is K a group with the binary operation of composition?
*3/10: Turn in [http://helmut.knaust.info/class/202620_4303/WS03.pdf Worksheet 3], Problems 5-7, next time ('''one''' solution per team)
*3/5: Read 2.2.1-2.2.2. Problems 2.2.2: 1cd,4,6,7,12 (use <math>a=1+i\sqrt{3}</math> instead),13,15
*2/24: Read 2.2.1-2.2.2. Problems 2.2.1: 1bdef,2b,4
*2/19: Read 2.2.1-2.2.2. Problems: (1) Find the multiplicate inverse of <math>2-\sqrt{3}\,i</math>. (2) Show <math> \overline{y\cdot z}=\bar{y}\cdot\bar{z}</math> for all complex numbers y and z. (3) Find the square roots of <math>3-{\color{red}4}i</math>.
*2/12: Read 2.1.4, 2.2.1. Problems 2.1.4: 1ac,5cd,8ab,11
*2/10: Read 2.1.4.
*2/5: Show: Every number with a terminating or periodic decimal expansion can be written as a fraction.
*2/3: Read 2.1.3. Problems 2.1.3: 4abe,5abc,6ab,8
*1/28: Read 2.1.1.-2.1.2. Problems 2.1.1: 3ab,8,9a,10b,12ab & 2.1.2: 1
*1/26: (1) Turn in Worksheet 1 next time ('''one''' solution per team) (2) Find a non-Abelian group.

==Materials==
[http:///helmut.knaust.info/class/202620_4303/Manoucheri.pdf An In-class Conversation] | [http://helmut.knaust.info/class/201820_4303/Manouchehri_2003.pdf A. Manouchehri, D.A. Lapp, Unveiling Student Understanding: The Role of Questioning in Instruction, Mathematics Teacher Vol. 96 (2003)] |
[http://helmut.knaust.info/class/202520_4303/Riemann.nb Riemann Sphere] |
[http:///helmut.knaust.info/class/202620_4303/Papick.pdf ''Questions for Algebra Teachers'', by Ira J. Papick] | [http://helmut.knaust.info/Latex/Isometries/iso.pdf Isometries of the Complex Plane] |
[http://www.geogebratube.org/material/show/id/35697 A GeoGebra applet uploaded to ''GeoGebraTube''] (quartic) | [http://helmut.knaust.info/class/202620_4303/Roots.nb Roots of a parametrized quadratic polynomial] | [http://helmut.knaust.info/class/202620_4303/Quiz01.pdf Quiz 1] | [http://helmut.knaust.info/class/202220_4303/irrational_niven.pdf ''A simple proof that π is irrational''.] Bull AMS 53 (1947), 509. | [http://helmut.knaust.info/class/202520_4303/27&37.nb 27&37] | [http://helmut.knaust.info/class/202620_4303/DigitRepresentation.nb Digit Representation] | [http://helmut.knaust.info/class/202520_4303/DecimalRepresentation.nb Decimal Representation] | [https://en.wikipedia.org/wiki/Niels_Henrik_Abel Niels Henrik Abel] | [http://helmut.knaust.info/class/202620_4303/WS01.pdf Worksheet 1] | [http:///helmut.knaust.info/class/202620_4303/Abs-In.mp4 Video: Absolute Value Inequality] | [https://view.teachforamerica.org Teach for America (next deadline 2/2/26)]

CRN 22268

2026-03-31T22:46:22Z

HelmutKnaust: /* Materials */

==Syllabus for Math 4303==
''The greatest danger for most of us is not'' 
''that our aim is too high and we miss it,'' 
''but that it is too low and we reach it. ''
(Michelangelo Buonarroti)
* '''Time and Place.''' TR 15:00-16:20, CRBL C201.
__NOTOC__
* '''Instructor.''' Dr. Helmut Knaust, Bell Hall 219, [mailto:hknaust@utep.edu hknaust@utep.edu], (915) 747-7002

* '''Office Hours.''' M 15:00-16:00, TR 16:30-17:30, or by appointment.

* [[image:MfHST.jpg|right]]'''Textbook. ''' Zalman Usiskin, Anthony L. Peressini, Elena Marchisotto, and Dick Stanley. ''Mathematics for High School Teachers - An Advanced Perspective.'' Prentice Hall. ISBN-13 978-0130449412 (paperback). '''A PDF version of the textbook is available at https://knowledge.uchicago.edu/record/5793.''' The textbook is required at all class meetings, and the parts covered in class are intended to be read in full.

* '''Course Requirements.'''
** ''Quizzes, etc.(15%)'': I will give regular, but unannounced quizzes in class. Quiz problems will be identical to prior homework assignments. There will also be some other assignments (worksheets, writing assignments). Your worst two grades will be dropped.
** ''Exams (25% total)'': You will have two in-class exams on the following days: '''Tuesday, March 3''' and '''Thursday, April 30'''.
** ''Class Presentations (25%)'': Student pairs will each design and conduct all classroom activities for a class session and will be responsible for the content covered in that session. Each group will also create homework assignments.
*** The groups will meet with me two weeks before their presentation for a ''trial run'' so that I will know that you are prepared. This is not optional. If you do not meet with me, you will lose half of your possible points.
** ''Final Project (20%)'': There are mathematics problems that require more attention than just one day. Some of these problems are, for example, found at the end of the chapters in the textbook. Student groups will complete such a problem and present the results in class during the final period '''Thursday, May 14 at 16:00 – 18:45.'''
** ''Class Participation (15%)'': This is a Mathematics class, and, as you know, Mathematics is not a spectator sport. During class I expect you to participate. This is an active class where students daily present solutions to their peers. The participation grade will be based both on the quality and frequency of your contributions.
* '''Grades.''' Your grade will be based on the percentage of the total points that you earn during the semester. You need at least 90% of the points to earn an A, at least 80% for a B, at least 70% for a C, and at least 60 % for a D.

* '''Make-up Exams'''. Make-up tests will only be given under extraordinary circumstances, and only if you notify the instructor prior to the exam date. There will be no make-up quizzes.

* '''Time Requirement.''' I expect that you spend an absolute minimum of six hours a week outside of class on preparing your group activities, reading the textbook, preparing for the next class, reviewing your class notes, and completing homework assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.

* '''Attendance.''' Due to the nature of the course you are strongly encouraged to attend class every day. I expect you to arrive for class on time and to remain seated until the class is dismissed. Students with six or more absences (excused or unexcused) will be dropped from the course with a grade of "F".

* '''Mathematica.''' I will show in class and make available a few ''Mathematica'' notebooks. ''Mathematica'' is available at https://www.utep.edu/technologysupport/ServiceCatalog/SOFTWARE_PAGES/soft_mathematica.html. Choose "Mathematica Online", not "Mathematica"! I do not expect you to learn how to code, but if you want to learn more about writing ''Mathematica'' code, a nice but voluminous introduction to Mathematica can be found at [https://www.wolfram.com/language/elementary-introduction/ An Elementary Introduction to the Wolfram Language, by Stephen Wolfram].

* '''Drop Policy.''' The class schedule lists '''Thursday, April 2''', as the last day to drop with an automatic "W". After the deadline, I can only drop you from the course with a grade of "F".

* [https://capitol.texas.gov/tlodocs/89R/billtext/pdf/SB00037F.pdf Texas Senate Bill 37]. The 2025 law reshaping the governance of public colleges and universities, does not prohibit the teaching of any particular content in academic courses at public colleges and universities in Texas. Although earlier versions of the bill included censorship of specific course content, these provisions were removed in the final version. Expectations and academic freedom for teaching and class discussion have not been altered due to prohibitions in SB 37, and students should not feel the need to censor their speech pertaining to topics including race, gender, gender identity, ethnicity, politics, society, and religion.

* '''Academic Integrity.''' All students must abide by UTEP's academic integrity policies. For detailed information visit the Office of Student Conduct and Conflict Resolution (OSCCR) website. Academic Integrity is a commitment to fundamental values. From these values flow principles of behavior that enable academic communities to translate ideals into action.” Specifically, these values are defined as follows:
** Honesty: advances the quest for truth and knowledge by requiring intellectual and personal honesty in learning, teaching, research, and service.
** Trust: fosters a climate of mutual trust, encourages the free exchange of ideas, and enables all to reach their highest potential.
** Fairness: establishes clear standards, practices, and procedures and expects fairness in the interaction of students, faculty, and administrators.
** Respect: recognizes the participatory nature of the learning process and honors and respects a wide range of opinions and ideas.
** Responsibility: upholds personal responsibility and depends upon action in the face of wrongdoing.

* '''AI (Artificial Intelligence) Use.''' Use of AI technologies or automated tools, particularly generative AI such as ChatGPT or DALL-E, is only allowed with approval from the instructor '''before''' being used. Without permission, you will be expected to think creatively and critically to complete assignments without aid from these tools. If given permission to use any of these tools, students must properly cite and give full credit to the program used upon submission of the assignment.

* '''Military Service.''' If you are a military student with the potential of being called to military service and/or training during the course of the semester, contact the instructor as soon as possible.

* '''Counseling Center.''' You are encouraged to go to [https://www.utep.edu/student-affairs/counsel/ Counseling and Psychological Services] (202 Union West) for personal assistance as you work through personal concerns. Confidential counseling services are offered in English or in Spanish. The Center provides a Crisis Hotline at 747-5302.

* '''Disabilities.''' If you have a disability and need special accommodation, please contact the [https://www.utep.edu/student-affairs/cass/ Center for Accommodations and Support Services] (CASS). The Center aspires to provide students with accommodations and support services to help them pursue their academic, graduation, and career goals. Phone 747-5148. E-mail: cass@utep.edu.

==Final Presentations==
[http:///helmut.knaust.info/class/202620_4303/FProjects2026.pdf Final Projects] | [http://helmut.knaust.info/BD/Gallian.pdf Advice on Giving a Good PowerPoint Presentation], by Joseph Gallian. | [http://helmut.knaust.info/presentations/2008/20081018_GEPCTM/Mersenne.pdf A sample project: Mersenne Primes.]

==Lesson Presentations==
[http:///helmut.knaust.info/class/202620_4303/Pres.pdf Presentation Details and Assignments] | [http:///helmut.knaust.info/class/202620_4303/PresRubric.pdf Rubric for Presentations]

==Open Problems==
*3.1.1: 2abc,3bcd,6,8.
* '''I2''' Let G be the set of all isometries with a fixed point <math>z^*</math>, i.e., <math>G=\{f:\C\to \C\ | \ F \mbox{ is an isometry and } f(z^*)=z^*\}</math>. Show that G forms a group with the binary operation of composition.
* '''I3''' Let H be the set of all isometries <math>f:\mathbb{C}\to \mathbb{C}</math> of the form <math>f(z)=z_0+ z e^{i\theta}</math> for some <math>z_0\in\C</math> and <math>\theta \in \R</math>. Is H a group with the binary operation of composition?
* '''I4''' Let K be the set of all isometries <math>f:\mathbb{C}\to \mathbb{C}</math> of the form <math>f(z)=z_0+ \overline{z} e^{i\theta}</math> for some <math>z_0\in\C</math> and <math>\theta\in\R</math>. Is K a group with the binary operation of composition?
* 2.2.2: 6,7,13,15

==Homework==
*3/31 '''Lesson 1 (4/2)''': 4.1.1: 1, 4a,7a; 4.1.2: 1a,2b,3
*3/26: Read 3.1.1-3.1.2. Problems 3.1.1: 2abc,3bcd,6,8.
*3/12: (1) Let <math>f(z)=z_0+ z e^{i\alpha}</math> and <math>g(z)=z_1+ \overline{z} e^{i\beta}</math>. Compute their compositions <math>f\circ g</math> and <math>g\circ f</math>. (2) Let G be the set of all isometries with a fixed point <math>z^*</math>, i.e., <math>G=\{f:\C\to \C\ | \ F \mbox{ is an isometry and } f(z^*)=z^*\}</math>. Show that G forms a group with the binary operation of composition. (3) Let H be the set of all isometries <math>f:\mathbb{C}\to \mathbb{C}</math> of the form <math>f(z)=z_0+ z e^{i\theta}</math> for some <math>z_0\in\C</math> and <math>\theta \in \R</math>. Is H a group with the binary operation of composition? (4) Let K be the set of all isometries <math>f:\mathbb{C}\to \mathbb{C}</math> of the form <math>f(z)=z_0+ \overline{z} e^{i\theta}</math> for some <math>z_0\in\C</math> and <math>\theta\in\R</math>. Is K a group with the binary operation of composition?
*3/10: Turn in [http://helmut.knaust.info/class/202620_4303/WS03.pdf Worksheet 3], Problems 5-7, next time ('''one''' solution per team)
*3/5: Read 2.2.1-2.2.2. Problems 2.2.2: 1cd,4,6,7,12 (use <math>a=1+i\sqrt{3}</math> instead),13,15
*2/24: Read 2.2.1-2.2.2. Problems 2.2.1: 1bdef,2b,4
*2/19: Read 2.2.1-2.2.2. Problems: (1) Find the multiplicate inverse of <math>2-\sqrt{3}\,i</math>. (2) Show <math> \overline{y\cdot z}=\bar{y}\cdot\bar{z}</math> for all complex numbers y and z. (3) Find the square roots of <math>3-{\color{red}4}i</math>.
*2/12: Read 2.1.4, 2.2.1. Problems 2.1.4: 1ac,5cd,8ab,11
*2/10: Read 2.1.4.
*2/5: Show: Every number with a terminating or periodic decimal expansion can be written as a fraction.
*2/3: Read 2.1.3. Problems 2.1.3: 4abe,5abc,6ab,8
*1/28: Read 2.1.1.-2.1.2. Problems 2.1.1: 3ab,8,9a,10b,12ab & 2.1.2: 1
*1/26: (1) Turn in Worksheet 1 next time ('''one''' solution per team) (2) Find a non-Abelian group.

==Materials==
[http:///helmut.knaust.info/class/202620_4303/Manoucheri.pdf An In-class Conversation] | [http://helmut.knaust.info/class/201820_4303/Manouchehri_2003.pdf A. Manouchehri, D.A. Lapp, Unveiling Student Understanding: The Role of Questioning in Instruction, Mathematics Teacher Vol. 96 (2003)] |
[http://helmut.knaust.info/class/202520_4303/Riemann.nb Riemann Sphere] |
[http:///helmut.knaust.info/class/202620_4303/Papick.pdf ''Questions for Algebra Teachers'', by Ira J. Papick] | [http://helmut.knaust.info/Latex/Isometries/iso.pdf Isometries of the Complex Plane] |
[http://www.geogebratube.org/material/show/id/35697 A GeoGebra applet uploaded to ''GeoGebraTube''] (quartic) | [http://helmut.knaust.info/class/202620_4303/Roots.nb Roots of a parametrized quadratic polynomial] | [http://helmut.knaust.info/class/202620_4303/Quiz01.pdf Quiz 1] | [http://helmut.knaust.info/class/202220_4303/irrational_niven.pdf ''A simple proof that π is irrational''.] Bull AMS 53 (1947), 509. | [http://helmut.knaust.info/class/202520_4303/27&37.nb 27&37] | [http://helmut.knaust.info/class/202620_4303/DigitRepresentation.nb Digit Representation] | [http://helmut.knaust.info/class/202520_4303/DecimalRepresentation.nb Decimal Representation] | [https://en.wikipedia.org/wiki/Niels_Henrik_Abel Niels Henrik Abel] | [http://helmut.knaust.info/class/202620_4303/WS01.pdf Worksheet 1] | [http:///helmut.knaust.info/class/202620_4303/Abs-In.mp4 Video: Absolute Value Inequality] | [https://view.teachforamerica.org Teach for America (next deadline 2/2/26)]