Spring 2022 MAT 319: Foundations of AnalysisSpring 2022 MAT 320: Introduction to Analysis
ScheduleTuTh 11:30am-12:50pm S B Union 103-02 (through 3/1: joint lectures in S B Union 103-02)TuTh 11:30am-12:50pm Earth & Space 131 (through 3/1: joint lectures in S B Union 103-02)
InstructorLjudmila KamenovaRaanan Schul
Office hours LK's web card RS's web card
RecitationMW 2:40-3:35pm Earth & Space 181, Physics P-117MW 2:40-3:35pm Earth & Space 183
TAAlexandra Viktorova, Mohamed El AlamiOwen Mireles Briones
Office hoursViktorova's web card,
El Alami's web card
Mireles Briones's web card
Description A careful study of the theory underlying topics in one-variable calculus, with an emphasis on those topics arising in high school calculus. The real number system. Limits of functions and sequences. Differentiations, integration, and the fundamental theorem. Infinite series. A careful study of the theory underlying calculus. The real number system. Basic properties of functions of one real variable. Differentiation, integration, and the inverse theorem. Infinite sequences of functions and uniform convergence. Infinite series.
Overview The purpose of this course is to build rigorous mathematical theory for the fundamental calculus concepts, sequences and limits, continuous functions, and derivatives. We will rely on our intuition from calculus, but (unlike calculus) the emphasis will be not on calculations but on detailed understanding of concepts and on proofs of mathematical statements. An introductory course in analysis, it provides a closer and more rigorous look at material which most students encountered on an informal level during their first two semesters of Calculus. Students learn how to write proofs. Students (especially those thinking of going to graduate school) should take this as early as possible.
Prerequisites C or higher in MAT 200 or permission of instructor; C or higher in one of the following: MAT 203, 205, 211, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161.
Math majors are required to take either MAT 319 or MAT 320
TextbookBartle and Sherbert Introduction to Real Analysis, 4th edition
Homework Weekly problem sets will be assigned, and collected in the Wednesday recitation. The emphasis of the course is on writing proofs, so please try to write legibly and explain your reasoning clearly and fully. You are encouraged to discuss the homework problems with others, but your write-up must be your own work.
Late homework will never be accepted, but under documented extenuating circumstances the grade may be dropped. Your lowest homework grade will be dropped at the end of the class.
GradingHomework: 20%, Midterm I: 20%, Midterm II: 20%, Final: 40%.

Syllabus/schedule (subject to change)
All joint lectures through 3/1 meet in S B Union 103-02.
The first recitation is on Wed 1/26.

Recommendations on choosing MAT 319 vs MAT 320 will be made based upon your performance on the first midterm and homework to that date.
Discussion Board: If you log on to Blackboard then you can use the Discussion Board.

Tue 1/251. Joint class: Sets, induction (Schul)Read Sections 1.1-1.3 and do Homework #1 on Blackboard
Thu 1/272. Joint class: Infinite sets. (Kamenova)HW due 2/2: p.10 #5, 6, p.15 #2, 9, p.22 #4
Tue 2/13. Joint class: Algebraic properties of the real numbers. (Schul)Read Sections 2.1-2.3
Thu 2/34. Joint class: Completeness of the real numbers. (Kamenova)HW due 2/9: p.30 #8, 15, p.35 #3, 16, p.39 #6
Tue 2/8 5. Joint class: Applications of the supremum property (Schul)Read Sections 2.4-2.5
Thu 2/106. Joint class: Intervals. (Kamenova)HW due 2/16: p.45 #2, 4, 7, p.52 #3, 6
Tue 2/157. Joint class: Sequences and limits. (Schul)Read Sections 3.1-3.2
Thu 2/178. Joint class: Limit theorems. (Schul)HW due 3/2: p.61 #6, 8, 9, p. 69 #6, 16
Tue 2/229. Joint class: Monotone sequences. (Kamenova)Read Sections 3.3-3.4
Thu 2/24 Joint Midterm I in SB Union 103-02.
Tue 3/110. Joint class: Subsequences and the Bolzano-Weierstrass Theorem (Schul) Read Section 3.4
Thu 3/311. Joint class: Cauchy's criterion (Kamenova) Read Section 3.5. HW due 3/9: p.77 #1, 7, p.84 #1, p.91 #5, 8

The following syllabus below is only for MAT 319, in S B Union 103-02
Tue 3/812.Divergent sequencesRead Sections 3.6, 3.7.
Thu 3/1013.Infinite seriesHW due 3/23: p.93 #5, 8, p.100 #3, 9, 11
Tue 3/15 Spring Break
Thu 3/17 Spring Break
Tue 3/2214.Limits of functionsRead Sections 4.1,4.2.
Thu 3/2415.Limit theoremsHW due 3/30: p.110 #1, 6, p.116 #2, 3, 4
Tue 3/2916.Continuous functions and combinations of continuous functionsRead Sections 5.1-5.3.
Thu 3/3117.Continuous functions on intervalsHW due 4/13: p.129 #7, 12, p.133 #2, 7, p.140 #6
Tue 4/518.Uniform continuityRead Section 5.4.
Thu 4/7 Midterm II in class
Tue 4/1219.Monotone and inverse functionsRead Sections 5.6, 6.1.
Thu 4/1420.DerivativeHW due 4/20: p.148 #7, p. 160 #1, 5, p.171 #7
Tue 4/1921.Mean Value TheoremRead Sections 6.2, 6.3.
Thu 4/2122.L'Hospital's ruleHW due 4/27: p.179 #6, 13, p.187 #5, 6, 7
Tue 4/2623.Taylor's TheoremRead Sections 6.4, 7.1.
Thu 4/2824.Riemann integralHW due 5/4: p.196 #1, 4, 5, p.207 #8, 15
Tue 5/325.Riemann integrable functionsRead Sections 7.2, 7.3.
Thu 5/526.Fundamental theorem of calculus
Final Exam: Tuesday May 17, 11:15AM-1:45PM

Disability Support Services: If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact Disability Support Services (DSS) office: ECC (Educational Communications Center) Building, room 128, telephone (631) 632-6748/TDD. DSS will determine with you what accommodations are necessary and appropriate. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability is confidential. Students requiring emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information, go to the following web site http://www.ehs.sunysb.edu and search Fire safety and Evacuation and Disabilities.

Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instance of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/.

Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, and/or inhibits students' ability to learn.