개인 공부 정리용도로 제작한 자료입니다. 주된 참고자료는 Stein 3권 Real analysis이고 부수적으로 Folland책을 참고하였습니다. Last update : 2024/8/14

[에브리유니즈 체험단 협찬 후기]기존에 키크론 K8 청축 모델을 2020년도에 구매하여 사용하던 중, B1 pro 체험단 모집글을 확인하게 되었고, 당첨이 됨에 따라 해당 모델에 대한 후기를 남기도록 하겠습니다.제품 구성은 다음과 같습니다.키보드 유형은 펜타그래피이고, 숫자패드가 없는 버젼이라서 콤팩트하게 가방에 들고 다닐 수 있는 정도의 크기를 가지고 있습니다.K8 청축 키보드의 경우 기계식 키보드에 속하는 것으로 직접적인 비교는 어렵겠지만, B1 모델과 비교했을 때 다음과 같은 장단점을 가지고 있습니다.장점들고 다니기 굉장히 편입니다. K8 모델의 경우, 들고 다니면서 사용하기에는 많이 불편한데 이 모델의 경우에는 충분히 들고다니면서 움직일만 한 것 같습니다.소음이 굉장히 적은 편입니다. 연구실에서 ..

Last update : 2024.5.11

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Norm approximationBasic norm approximation problemAssume that the columns of AAA are independent.minimize ∥Ax−b∥\text{minimize }\|Ax - b\| minimize ∥Ax−b∥where A∈Rm×nA\in \R^{m\times n}A∈Rm×n with m≥nm\ge nm≥n, ∥⋅∥\|\cdot\|∥⋅∥ is a norm of Rm\R^mRmGeometric interpretationGeometrically, the solution x∗x^*x∗ is the point such that Ax∗∈R(A)Ax^*\in \mathcal R(A)Ax∗∈R(A) that closest to bbb. ..

LagrangianThe basic idea in Lagrangian duality is to take the constraints into account by augmenting the objective function with a weighted sum of the constraint functions.💡By using the Lagrangian, we can get a hint to solve the original problem which is not convex nor easy to solve.Standard form problem (not necessary convex)minimize f0(x)\text{minimize }f_0(x)minimize f0​(x)subject tofi(x)≤0i=..

Optimization problem in standard formminimize f0(x)\text{minimize } f_0(x)minimize f0​(x)subject tofi(x)≤0,  i=1,…,mhi(x)=0,  i=1,…,pf_i(x) \le 0, \; i = 1, \dots, m \\ h_i(x) = 0, \; i = 1, \dots, pfi​(x)≤0,i=1,…,mhi​(x)=0,i=1,…,px∈Rnx\in \R^nx∈Rn is the optimization variablef0:Rn→Rf_0:\R^n\to \Rf0​:Rn→R is the objective or cost functionfi:Rn→R,  i=1,…,mf_i:\R^n\to \R, \; i = 1, \dots, mfi​:R..

Convex functionf:Rn→Rf:\R^n \to \Rf:Rn→R is convex if dom f\text{dom }f dom f is a convex set andf(θx+(1−θ)y)≤θf(x)+(1−θ)f(y)f(\theta x + (1 - \theta)y ) \le \theta f(x) + (1-\theta)f(y)f(θx+(1−θ)y)≤θf(x)+(1−θ)f(y)for all x,y∈dom f,0≤θ≤1x, y\in \text{dom }f, 0 \le\theta \le 1x,y∈dom f,0≤θ≤1fff is strictly convex if dom f\text{dom }fdom f is convex andf(θx+(1−θ)y)θf(x)+(1−θ)f(y)f(\theta x +..

Affine setLine : all points through x1,x2x_1, x_2x1​,x2​x=θx1+(1−θ)x2x = \theta x_1 + (1 - \theta) x_2x=θx1​+(1−θ)x2​where θ∈R\theta\in \Rθ∈RThis idea can be generalized to more than two points.θ1x1+θ2x2+⋯+θkxk\theta_1x_1 + \theta_2 x_2 + \cdots + \theta_kx_kθ1​x1​+θ2​x2​+⋯+θk​xk​where θ1+⋯+θk=1\theta_1 + \cdots + \theta_k = 1θ1​+⋯+θk​=1We refer to a point can be expressed as the following fo..

Mathematical optimizationmin⁡xfo(x)s.t fi(x)≤bi, i=1,…,m\begin{align}\min_x & f_o(x) \\ \text{s.t }& f_i(x) \le b_i, \ i = 1, \dots, m\end{align}xmin​s.t ​fo​(x)fi​(x)≤bi​, i=1,…,m​​wherex=(x1,…,xn)x = (x_1, \dots, x_n)x=(x1​,…,xn​): optimization variablesfo:Rn→Rf_o : R^n \to Rfo​:Rn→R: objective function (a.k.a the function we want to minimize)💡In deep learning or machine learning perspective..

Creating and Dropping usersTo create a user in MySQLUsername user can be followed by @ and the IP or the hostname from which the user is allowed to log in. Example:To drop a user: DROP USER userAuthorizationcontrol of what users can do in the database what they can see, create, modify, delete etcExercise 1What privileges are needed to be able to execute the following query?Answer:UPDATE (graduat..

IndexMotivationMySQL database, 10,000,000 peopleHow long does it take to find name and phone number for person with ID 4,857,845?How long does it take to find the phone number for all people named Kristin Elvik?The result of the second experiment is very slow. Why is it slow and what can we do about it?ExplanationThe slow query from the experiment performs a full table scan each row in the table..

Simple selectattribute : specifies a column in the resulttable_reference : the name of the tablewhere_condition : the condition that selected rows must satisfyExampleSelect DistinctTo remove duplicate rows from the result, we can use SELECT DISTINCTWhere ClauseLogical connections AND , OR , NOT can be used to create a more complex where conditionIS [NOT] NULLIS NULLIS NOT NULL💡NEVER use NULL nor..

Issues with DBMS DesignData integrity failure : e.g. key doesn’t exists💡앞 장에서 다룬 integrity constraint의 경우에는 위의 data integrity가 깨지지 않는 것을 보장하는 것이고, normalization은 data integrity가 보존되게끔 data base를 design한다는 의미라고 이해하면 된다.NormalizationThe process of breaking bad relations/tables smaller good relations→ leads to a better DB designAvoids updating, deleting, and inserting anomaliesThe normalization pro..

Regular Entity MappingMap each Regular Entity to a Relation with all simple attributesUnpack composite attribute💡즉 다시 말해서 name를 따로 column으로 만드는 것이 아니라 나머지만 취급하면 된다는 것이다.A primary key can also be a composite keyex : country code, car number💡아직 multivalued attribute를 어떻게 다룰 지에 대해서는 논의하지 않음Mapping of one-one Relation3 possible waysForeign key : Better to choose an entity with total participation→ 위..

Converting ER to DBMS TablesProblem: This entity relationship does not have 1-1 direct mapping. So we can’t convert it directly💡예를 들어서 relationship같은 경우 어떻게 처리하고 저장할 것인지에 대해서는 ER model이 답하지 않는다. 따라서 DBMS table과 ER이 direct mapping되지 않는다는 것이다.그래서 Relational Data model 이 등장하게 된 것이다.💡Relational Model은 DBMS와 direct mapping할 수 있다.A Relation주의할 점은 Relationship와 relation은 구분해야한다는 것이다.Relationship: Entit..