===== Linear Algebra - Math 304 ===== === Spring 2021 - Course Coordinator: Prof. Alex Feingold === ^Sec^Instructor^Office^Email(*)^Meets^Room| |1|Matthew Haulmark|online|[[matthew@math.binghamton.edu|Haulmark]]|MWF:8:00-9:30|online| |2|Michael Dobbins|online|[[dobbins@math.binghamton.edu|Dobbins]]|MWF:8:00-9:30|online| |3|David Biddle|online|[[biddle@binghamton.edu|Biddle]]|MWF:9:40-11:10|online| |4| | | | | | |5|[[http://people.math.binghamton.edu/grads/eppolito/math304-s21/|Christopher Eppolito]]|online|[[eppolito@math.binghamton.edu|Eppolito]]|MWF:11:20-12:50|online| |6|[[http://people.math.binghamton.edu/alex/Math304-6_Spr2021.html|Alex Feingold]]|online|[[alex@math.binghamton.edu|Feingold]]|MWF:1:10-2:40|online| |7|Thomas Kilcoyne|online|[[kilcoyne@math.binghamton.edu|Kilcoyne]]|MWF:2:50-4:20|online| |8|Thomas Kilcoyne|online|[[kilcoyne@math.binghamton.edu|Kilcoyne]]|MWF:4:40-6:10|online| (*): To send an email to your instructor, click on the link in the Email column of the table. If a section has its own detailed syllabus webpage, a link to that page will be provided under the Instructor column of the table above. Each instructor should provide their students with a Zoom link to the recurring class meetings which begin on Friday, Feb 12, and end on Monday, May 17, 2021. Below is a partial syllabus with information for all sections that you should know. Your instructor may have a more detailed syllabus about how your section will be run. === Textbook === ``Linear Algebra" by Jim Hefferon, Fourth Edition, available as a free download here: [[http://joshua.smcvt.edu/linearalgebra/book.pdf|Linear Algebra by Jim Hefferon]]. On can buy a cheap printed version and access more free resources at the [[https://hefferon.net/linearalgebra/index.html|textbook's official website]]. Here are also some additional books that students and instructors may find helpful. [[http://linear.ups.edu/download/fcla-3.50-tablet.pdf|A First Course in Linear Algebra by Robert A. Beezer]] [[http://www.numbertheory.org/book/mp103.pdf|Elementary Linear Algebra by K.R. Matthews]] [[https://www.math.ucdavis.edu/~linear/linear-guest.pdf|Linear Algebra by D. Cherney, T. Denton, R. Thomas, and A. Waldron]] === Approximate Exam Schedule (Each section instructor will decide when it is appropriate to give Exams 1, 2, 3.) === Exam 1: The week of March 8-12. Exam 2: The week of April 12-16. Exam 3: The week of May 10-14. Final Exam: Tuesday, May 25, 8:00 - 10:00 AM Online. === Grades === Remote format of the course requires steps to combat academic dishonesty and to protect the honest students from unfair competition. Details about how quizzes and exams will be administered so as to achieve that goal will be announced by your instructor. Your instructor may decide to use: (1) Limited time to answer each question, (2) Visual observation of you during the exam through Zoom, (3) Oral exams in place of, or in addition to, written exams. Some advice about preparing for oral exams is available through the following link: [[http://people.math.binghamton.edu/borisov/MATH304Fall20/StudyForOralExams.pdf |How to study for oral exams]] The course total will be determined as follows: Quizzes: 20% Exam 1: 20% Exam 2: 20% Exam 3: 20% [[https://webwork.math.binghamton.edu/webwork2/304Spring2021/ |WebWork Homework]] (common for all sections): 5% Final Exam: 15% At the end of the course, your grade in the course will be determined by your instructor based on your course total and the following approximate scale. (Borderline cases will be decided by other factors such as attendance or participation.) A 90%, A- 85%, B+ 80%, B 75%, B- 70%, C+ 65%, C 55%, C- 50%, D 45% === Homework === Online homework will be done using WebWork. The server address is https://webwork.math.binghamton.edu/webwork2/304Spring2021/ For students, your WebWork account username is the pre@ portion of your binghamton.edu e-mail account. Your initial password is the same as the username. For example, if your Binghamton e-mail account is xyzw77@binghamton.edu then your username is: xyzw77 and your initial temporary password is: xyzw77 **Make sure to change your password as soon as possible to a secure password, and save that choice where it will not be lost.** **Important:** Besides the WebWork homework sets, you should do problems from the book, as selected by your instructor, see an approximate schedule below. This part of the homework will not be graded, but it will be important to your success in the course. === Expected workload === You are expected to spend about 12.5 hours per week on average for this class, including participation in Zoom lectures, watching instructional videos, solving homework problems (graded and ungraded), reviewing the material, and preparing for the tests. Expect the work load to be higher than average in the weeks before the exams. === Expected behavior in class === During online classes all students are expected to participate in a way that maximizes their learning and minimizes disruptions for their classmates. Your instructor has the final word on the use of video and audio in the general Zoom sessions, break-out rooms, and online office hours. If you have any concerns, limitations, or circumstances, please communicate with your instructor to find the most appropriate solution. === Academic Code of Honor === For all graded assignments and exams, you are not allowed to use any help not explicitly authorized by your instructor. This includes, but is not limited to, problem-solving websites, notes, help from other people, etc. All instances of academic dishonesty will be investigated, penalized, and referred to the appropriate University officials for maximal possible punishment. In other words, **don't even think of trying to cheat.** === Getting Help === If you fall behind in class, or need extra help to learn the material, talk to your instructor as soon as you can. They should be able to help you and also point you to other resources. We also encourage you to talk to your classmates, and, in particular, to form informal study groups to prepare for the exams. === Disability Information === If you have a disability for which you are or may be requesting an accommodation, please contact both your instructor and the Services for Students with Disabilities office (119 University Union, 607-777-2686) as early in the term as possible. Note: extended time for the examinations may not automatically apply to the interview-style exams, but we will work with you to provide reasonable accommodations that are appropriate for your situation. ==== Suggested problems from our textbooks ==== The table below contains suggested problems from sections of our textbooks (Heffron or Matthews) in the format "Chapter:Section.Subsection.ProblemNumber". Your instructor may suggest other problems or exercises. **These problems are for practice only and are not to be turned in.** There will be graded homework assignments given through WebWork which should be done in the order indicated by your instructor. Instructional videos linked below are **supplementary material**, not intended to replace the regular lectures. The order in which material is presented in class meetings will be determined by your instructor, and may not precisely follow the order in our textbooks. ^ Topics ^ Text ^ Problems ^ |Introduction, preview, examples; linear combination | Ch. 1, I.1 | 1:I.1.17,19,21 | |Gaussian elimination (reduction) | Ch. 1, I.1 | 1:I.1.22,24,27,32 | |(Augmented) matrix of a system, solution set | Ch. 1, I.2 | 1:I.2.15,16,17,18,21,25 | |Basic logic: statements, connectives, quantifiers | Appendix | | |Set theory, general functions | Appendix | | | Homogeneous and non-homogeneous systems (no formal induction in Lemma 3.6)| Ch. 1, I.3 |1:I.3.15,17,18,20,21,24 | | Points, vectors, lines, planes | Ch. 1, II.1 | 1:II.1.1,2,3,4,7 | | Distance, dot product, angles, Cauchy-Schwarz and Triangle Inequalities | Ch. 1, II.2 | 1:II.2.11,12,14,16,17,21,22 | | Gauss-Jordan reduction, reduced row echelon form | Ch. 1, III.1 | 1:III.1.8,9,10,12,13,14,15 | | Linear combination lemma, uniqueness of RREF (no proofs of 2.5, 2.6) | Ch. 1, III.2 | 1:III.2.11,14,20,21,24 | | Review| Ch. 1; Appendix | [[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam1_Student_Info.pdf |Student's_Guide]]; [[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam1SampleProblems.pdf |Sample_Problems]]; [[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam1Sample_Solutions.pdf |Solutions]]| | Matrix operations, including the transpose. Linear system as a matrix equation | Matthews 2.1 | 3:III.1.13,14,15,16 | | Linear maps (transformations) given by matrices | Matthews 2.2 | 3:III.1.19; 3:III.2.12,17,30| | Vector spaces: definition, examples | Ch. 2, I.1 | 2:I.1.17,18,19,21,22,29,30 | | Linear maps between vector spaces | Ch. 3, II.1 | 3:II.1.18,19,20,22,24,25,26,28 | | Subspaces. Span | Ch. 2, I.2 |2:I.2.20,21,23,25,26,29,44,45 | | Linear independence | Ch. 2, II.1 | 2:II.1.21,22,25,28 | | Properties of linear independence | Ch. 2, II.1 | 2:II.1.29,30,32,33 | | Basis of a vector space | Ch. 2, III.1 | 2:III.1.20,21,22,23,24,25,26,30,31,34 | | Dimension of a vector space | Ch. 2, III.2 | 2:III.2.15,16,17,18,19,20,21,24,25,28| | Column space, row space, rank | Ch. 2, III.3 | 2:III.3.17,18,19,20,21,23,29,32,39 | | Range space and Kernel (Null space)| Ch. 3, II.2 | 3:II.2.21,23,24,26,31,35 | | Review | |[[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam2_Student_Info.pdf |Student's_Guide]]; [[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam2SampleProblems.pdf |Sample_Problems]]; [[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam2Sample_Solutions.pdf |Solutions]] | |Invertible matrices: definition, equivalent conditions; inverse matrix |Ch.3, IV.4 |3:IV.4.13,14,15,16,17,18,19,26,29 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=891abfd4-ec0b-4d50-bfed-ab87011501d4|InvertibleMatrices_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=ca18077c-0689-439f-af66-ab8701151767|InvertibleMatrices_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=4462a425-e0d1-44d8-a8ab-ab8800c0422e|InvertibleMatrices_3]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=61042f10-2740-4624-be7a-ab8800e1a912|InvertibleMatrices_4]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=455a2db2-c9ec-4549-83ca-ab8800e1d124|InvertibleMatrices_5]]| | Elementary matrices. Row reduction using elementary matrices |Ch. 3, IV.3; CDTW Ch. 2, 2.3 |3:IV.3.24,25,32 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=9993501d-2715-4570-9170-ab89015b2cd1|ElementaryMatrices_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=2933180e-cdba-453b-8a56-ab89015b4796|ElementaryMatrices_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=18983b6f-62e2-4574-a86a-ab89015b6218|ElementaryMatrices_3]]| | Determinant of a matrix, properties | Ch. 4, I.1, I.2 | 4:I.1.1,3,4,6,9; 4:I.2.8,9,12,13,15,18 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=13cb16b7-5ba2-46ef-898b-ab8b0156ffd7|Determinants_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=37d3c74f-6078-4ffa-8115-ab8b01571e2a|Determinants_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=70bd0381-7c62-4878-94df-ab8b01573231|Determinants_3]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=8226dbdd-8f17-4fbb-9d93-ab8b01574969|Determinants_4]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=0f291b37-9ba5-432e-8ced-ab8b015771c8|Determinants_5]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=2f04185f-64e3-4094-8fee-ab8b015777b2|Determinants_6]] | | More on Determinants |Ch. 4, II.1, III.1| 4:III.1.11,14,16,17,20,21,22 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=b92dec9b-cf5e-44d8-9da7-ab8e0136cb22|Determinants_7(Cramer)]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=55ed3990-2adc-4452-9e7a-ab8e0136d910|Determinants_8(Adjoint)]]| | Matrix of a linear transformation, matrix of the composition, inverse|Ch. 3, III.1, IV.2 |3:III.1.13,17,18,19,21,23 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=8202c2be-1166-46d8-a42e-ab8e0136f685|Matrix_of_Transformation_1]] | | Change of basis, similar matrices |Ch. 3, V.1, V.2; Ch. 5, II.1 |3:V.1.7,9,10,12; 5:II.1.5,8,11,13,14 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=7d82ec6d-e3c9-47f3-b910-ab8e013706a8|Matrix_of_Transformation_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=4c00a82d-6ff3-4c7f-a22f-ab8e01370fa6|Matrix_of_Transformation_3]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=a18c341c-82fe-4893-aa59-ab8e01371655|Matrix_of_Transformation_4]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=44835249-d45a-4c9a-93c3-ab9200dbe58f|Similar_Matrices]] | | Complex numbers |Matthews 5.1--5.6 |Matthews 5.8.1,2,5,6,7,9 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=fbc60b26-7b98-4a0f-b676-ab9701426658|Complex_Numbers_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=947058b8-d845-43ea-8bcf-ab9701426cb6|Complex_Numbers_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=29fc4ef8-943e-45d4-824c-ab9701427331|Complex_Numbers_3]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=e3ae74ea-f44d-4592-8388-ab970142789d|Complex_Numbers_4]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=285f677c-5e10-42dc-957e-ab9701428869|Complex_Numbers_5]] | | Eigenvectors, eigenvalues, eigenspaces for matrices and linear operators. Characteristic polynomial |Matthews 6.1, 6.2; Ch. 5, II.3|5:II.3.23,24,25,26,27,28,29,30,31 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=a7c14e1a-ada3-4a61-85db-ab9a002169ee|Eigenvectors_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=9824b1e8-7335-41e0-bcd6-ab9a002170c8|Eigenvectors_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=e93e85f3-baad-45f8-9c53-ab9a002175b1|Eigenvectors_3]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=8a0e45e3-0f1c-401a-a11f-ab9a00217b7c|Eigenvectors_4]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=5f6050c5-e4f1-4613-b0fe-ab9a00218c86|Eigenvectors_5]] | | Diagonalization of matrices |Ch. 5, II.2, II.3 |5:II.3.22,33,36,46 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=11b8a489-4a13-40f1-8c14-ab9c00141323|Diagonalization_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=ed9d04e0-e026-45ee-ac63-ab9c00141d29|Diagonalization_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=b1bcba95-ae59-43ce-a598-ab9c001422f4|Diagonalization_3]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=e6153328-2835-4fed-b593-ab9c00142938|Diagonalization_4]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=6b8895a4-7adf-41a6-a19e-ab9c00144249|Diagonalization_5]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=fcb5ba0c-7e0d-4d05-bdd8-ab9c00146341|Diagonalization_6]] | | Orthogonal and orthonormal bases of $R^n$ and its subspaces; orthogonal matrices |Ch. 3, VI.1, VI.2 |3:VI.1.6,7,17,19; 3:VI.2.10 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=cffa4bd8-53af-4993-b650-aba601062efa|Orthogonal_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=edfe91c1-d310-489d-bd53-aba601063785|Orthogonal_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=6b07dec4-c23e-4b02-9b35-aba601063ccb|Orthogonal_3]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=926ad2a6-bed6-4afe-adcd-aba6010642a4|Orthogonal_4]]| | Orthogonal complement of a subspace, orthogonal projection|Ch. 3, VI.3 |3:VI.3.11,12,13,14,26,27 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=326c1d70-1d6b-4e0a-983f-aba90151d9dd|Complements_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=088dbd48-935a-4695-afdd-aba90151e146|Complements_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=3e3e7b20-6a0e-4a7d-9ecd-aba90151ebf8|Complements_3]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=12687534-77aa-49e5-a894-aba90151f296|Complements_4]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=96b7b3de-836c-4709-899e-aba90151f80a|Complements_5]] | | Gram-Schmidt process; orthogonal diagonalization of matrices|Ch. 3, VI.2 |3:VI.2.13,15,17,18,19,22 [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=083e4724-7f94-4484-aea1-abaa00f9c6b5|GramSchmidt_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=aa14b784-dae9-4f61-91bd-abaa00f9cd02|GramSchmidt_2]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=2c2f5f0f-ff2e-49c4-b279-abaa00f9d46e|OrthogonalDiagonalization_1]] [[https://binghamton.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=1d0d2f8c-ef81-45bb-a3a5-abaa00f9d9cb|OrthogonalDiagonalization_2]] | |Review for Final Exam | | [[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam3_Student_Info.pdf |Student's_Guide]]; [[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam3_book_problems.pdf |Sample_Book_Problems]]; [[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam3SampleProblems.pdf |Sample_Problems]]; [[http://people.math.binghamton.edu/borisov/MATH304Fall20/Exam3Sample_Solutions.pdf |Solutions]]| === Sample Exams and Other Study Materials === **IMPORTANT:** Please note that the sample exams below are **traditional** written exams. Our interview-style exams will focus more on understanding and less on calculations. **Examination 1** [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt1sample1.pdf|Sample_1]],[[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt1sample1_ans.pdf|Answers_1]]; [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt1sample2.pdf|Sample_2]],[[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt1sample2_ans.pdf|Answers_2]]; [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt1sample3.pdf|Sample_3]],[[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt1sample3_ans.pdf|Answers_3]] **Examination 2** Being **cumulative**, Examination 2 will cover all the material of Examination 1 as well as additional topics: [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt2sample1.pdf|Sample_1]],[[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt2sample1_ans.pdf|Answers_1]]; [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt2sample2.pdf|Sample_2]],[[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt2sample2_ans.pdf|Answers_2]]; [[http://people.math.binghamton.edu/borisov/304_SecondExam_PracticeProblems.pdf|Some_Practice_Problems]], [[http://people.math.binghamton.edu/borisov/304_SecondExam_PracticeProblems_ans.pdf|Answers]] **Examination 3 and Final Examination** Being **cumulative**, Examination 3 and Final Examination will cover all the material of Examinations 1 and 2 as well as additional topics: [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt3sample1.pdf|Sample_1]], [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt3sample1_ans.pdf|Answers_1]]; [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt3sample2.pdf|Sample_2]], [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt3sample2_ans.pdf|Answers_2]]; [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt3sample3.pdf|Sample_3]], [[http://people.math.binghamton.edu/borisov/MATH304_Sp2020_mt3sample3_ans.pdf|Answers_3]] The following sample exams are traditional cumulative final exams. They are adapted, with permission, from the collection of Dr. Inna Sysoeva [[http://people.math.binghamton.edu/borisov/MATH304final_sample1.pdf|Sample_1]], [[http://people.math.binghamton.edu/borisov/MATH304final_sample1_ans.pdf|Answers_1]]; [[http://people.math.binghamton.edu/borisov/MATH304final_sample2.pdf|Sample_2]], [[http://people.math.binghamton.edu/borisov/MATH304final_sample2_ans.pdf|Answers_2]]; [[http://people.math.binghamton.edu/borisov/MATH304final_sample3.pdf|Sample_3]], [[http://people.math.binghamton.edu/borisov/MATH304final_sample3_ans.pdf|Answers_3]]; [[http://people.math.binghamton.edu/borisov/MATH304final_sample4.pdf|Sample_4]], [[http://people.math.binghamton.edu/borisov/MATH304final_sample4_ans.pdf|Answers_4]]; [[http://people.math.binghamton.edu/borisov/MATH304final_sample5.pdf|Sample_5]], [[http://people.math.binghamton.edu/borisov/MATH304final_sample5_ans.pdf|Answers_5]] ---- === Syllabi from previous semesters === ---- The syllabus for Math 304 in Fall 2020 is available through this link: [[https://www2.math.binghamton.edu/p/math304/fall2020|Fall 2020 page]] ---- The syllabus for Math 304 in Fall 2019 is available through this link: [[https://www2.math.binghamton.edu/p/math304/spring2020|Spring 2020 page]] ---- The syllabus for Math 304 in Fall 2019 is available through this link: [[https://www2.math.binghamton.edu/p/math304/fall2019|Fall 2019 page]] ---- The syllabus for Math 304 in Spring 2019 is available through this link: [[http://people.math.binghamton.edu/dikran/304/|Math 304 Syllabus for Spring 2019]] ---- The syllabus for Math 304 in Fall 2018 is available through this link: [[https://www2.math.binghamton.edu/p/math304/fall2018|Fall 2018 page]]