MATH 115B
Linear Algebra
Description: Lecture, three hours; discussion, one hour. Requisite: course 115A. Linear transformations, conjugate spaces, duality; theory of a single linear transformation, Jordan normal form; bilinear forms, quadratic forms; Euclidean and unitary spaces, symmetric skew and orthogonal linear transformations, polar decomposition. P/NP or letter grading.
Units: 4.0
Units: 4.0
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Most Helpful Review
Spring 2019 - Prof Chernikov is a cool guy and I really enjoyed his math 115B class. During lecture, he teaches straight from the book. This was a good and bad thing in my opinion--good because I could re-read the book after lecture to ingrain the concepts in my head, but bad because I hate Friedberg's Linear Algebra book. Maybe I'm just not good at math but I really think that book is horrible. Anyways, Chernikov is funny and good at explaining concepts. He does go kind of fast, but its easy to go back and learn what you missed. As a class, I would say 115B is fairly challenging, but that's what made it great. If you have the chance to take 115B, take it. And if you can get a class with Chrenikov, do it.
Spring 2019 - Prof Chernikov is a cool guy and I really enjoyed his math 115B class. During lecture, he teaches straight from the book. This was a good and bad thing in my opinion--good because I could re-read the book after lecture to ingrain the concepts in my head, but bad because I hate Friedberg's Linear Algebra book. Maybe I'm just not good at math but I really think that book is horrible. Anyways, Chernikov is funny and good at explaining concepts. He does go kind of fast, but its easy to go back and learn what you missed. As a class, I would say 115B is fairly challenging, but that's what made it great. If you have the chance to take 115B, take it. And if you can get a class with Chrenikov, do it.
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Most Helpful Review
Winter 2024 - This was the most challenging math course I've ever taken. I took this course after receiving an A+ in Math 115A and was humbled; my advice is to only take this course if you love proofs, theory, and desire a challenge. The homework assignments are manageable, and the lectures are (for the most part) a heavy review of 115A content within a more theoretical framework. Lecture notes are great so attendance in lecture is not necessary unless you want to ask questions. The exams are extremely challenging and make up a majority of your grade. The homework and lectures on their own are not sufficient to prepare for the exams, so a strong understanding of all the theorems is absolutely necessary to pass. I would recommend concept mapping and discussing in a study group. Luckily, Kannan is a great guy and genuinely wants his students to succeed; he is more than willing to help if you reach out.
Winter 2024 - This was the most challenging math course I've ever taken. I took this course after receiving an A+ in Math 115A and was humbled; my advice is to only take this course if you love proofs, theory, and desire a challenge. The homework assignments are manageable, and the lectures are (for the most part) a heavy review of 115A content within a more theoretical framework. Lecture notes are great so attendance in lecture is not necessary unless you want to ask questions. The exams are extremely challenging and make up a majority of your grade. The homework and lectures on their own are not sufficient to prepare for the exams, so a strong understanding of all the theorems is absolutely necessary to pass. I would recommend concept mapping and discussing in a study group. Luckily, Kannan is a great guy and genuinely wants his students to succeed; he is more than willing to help if you reach out.
Most Helpful Review
Spring 2024 - The course was enjoyable overall and well organized. However, I don't think I learned as much as I could have for a few reasons: First, the class was much too computational for my taste, and felt more like a sequel to 33A than to 115A. Second, proofs often relied very heavily on unproven lemmas, where all the work lies in the proof of the lemma. We essentially skipped the proofs of most major results in this manner. For instance, our "proof" of the Spectral theorem presumed the existence of an orthonormal basis of eigenvectors, and the only work we did was finding the matrix decomposition corresponding to this basis. Despite these shortcomings, I still enjoyed the lectures as they were very clear and easy to follow. Homework and exams were also very well-made.
Spring 2024 - The course was enjoyable overall and well organized. However, I don't think I learned as much as I could have for a few reasons: First, the class was much too computational for my taste, and felt more like a sequel to 33A than to 115A. Second, proofs often relied very heavily on unproven lemmas, where all the work lies in the proof of the lemma. We essentially skipped the proofs of most major results in this manner. For instance, our "proof" of the Spectral theorem presumed the existence of an orthonormal basis of eigenvectors, and the only work we did was finding the matrix decomposition corresponding to this basis. Despite these shortcomings, I still enjoyed the lectures as they were very clear and easy to follow. Homework and exams were also very well-made.
Most Helpful Review
Spring 2020 - Professor Manning is a beast! Great explainer, super helpful (literally answered every question I had in the class, even if they weren't related to math at all), and genuinely cares about students. Also, he's an actual genius. He is insanely smart and just as kind. I would highly recommend taking this course with him (or really any course, to be honest). He's awesome. Godspeed Professor Manning.
Spring 2020 - Professor Manning is a beast! Great explainer, super helpful (literally answered every question I had in the class, even if they weren't related to math at all), and genuinely cares about students. Also, he's an actual genius. He is insanely smart and just as kind. I would highly recommend taking this course with him (or really any course, to be honest). He's awesome. Godspeed Professor Manning.
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