Let's get straight to the point, skipping the introductions.

Why Learn Calculus and Its Modern Significance

1. The Evolving Meaning of Calculus

In the past, calculus was learned as a simple mathematical tool (for calculating slopes, areas, volumes, etc.), but in modern times, it is used as a deeper concept.
The core of modern calculus is predicting the future using measurable data such as velocity.

Navigation provides three main pieces of data:
- Real-time speed
- Remaining distance
- Estimated time of arrival
Speed and distance are easy data to measure currently and are information from the past.
On the other hand, arrival time is difficult data that needs to be predicted.
Integrating speed using calculus allows us to predict the distance traveled.

This allows navigation systems to update our estimated time of arrival in real-time.

3. Using Calculus in Life Science Research

(1) Modeling Changes in Normal and Infected Cells

Normal cells continuously divide.
Infected cells are killed by the immune system.
This process can be expressed as a mathematical model (differential equation) to predict future changes.

(2) Results of the Mathematical Model

Intuitively, cell proliferation and changes in the infected state may seem simple, but
in reality, regular cycles (oscillations, repetitive ups and downs) occur.
The spread patterns of actual epidemics (e.g., COVID) are similar to this.
- If the number of confirmed cases decreases, it re-spreads.
- This is a phenomenon that can be proven mathematically.

4. Convergence of Financial Markets and Mathematical Prediction

Jim Simons used mathematical models in the financial markets to predict price fluctuations.
It can be mathematically explained why stock prices in the market do not rise or fall forever, but repeat a certain pattern.
In this way, calculus is not a simple calculation tool, but a powerful means of predicting the future.

< Summary >

Calculus is the study of predicting the future by using measurable information.
Navigation calculates the estimated time of arrival by integrating speed.
In life science, changes in normal and infected cells can be modeled with differential equations.
The spread of epidemics and fluctuations in the stock market have a certain cycle, which can be analyzed and predicted using calculus.

[More…]

"Modern Applications of Calculus" → https://nextgeninsight.net/?s=Calculus
"How Mathematics Understands the World" → https://nextgeninsight.net/?s=Mathematics

*YouTube Source: [이효석아카데미]

– 사람을 살리는 데에 수학이 필요하다고? 미적분으로 주식 방향까지 맞출 수 있다고?ㅣ김재경 교수 (카이스트 수리과학부, IBS 의생명수학그룹)

Okay, here's the English translation of the text, with "Next-Korea.com" replaced by "nextgeninsight.net/", and maintaining the original formatting.

Trump's Strategy and Changes in International Relations

Trump's Strategy

President Trump utilizes brinkmanship and the madman theory.
Adopts a method of maximizing negotiating power while pressuring allies.
Actively utilizes economic means such as imposing tariffs, economic sanctions, and export controls to pressure various countries.

Changes in Relations with Allies

1. Negotiations with Canada & Mexico

In 2024, President Trump announced tariff policies on Canada and Mexico.
Insertion of retaliatory tariff clauses: Additional tariffs may be imposed if these countries resist U.S. actions.
Demands for resolving border issues and the fentanyl problem, leading to negotiations.

2. Case of Colombia

President Trump responded strongly when Colombia blocked U.S. military aircraft from transporting immigrants.
Announcement of imposing a 25% tariff on all Colombian products → Warning of a 50% increase after one week.
Announcement of visa bans and freezing U.S. assets of government officials → Sanctions virtually at the level of a hostile nation.
Even existing allies may face strong pressure from President Trump's negotiation strategies, increasing the possibility of friction.

Trump's Second Term and South Korea's Strategy

1. South Korea's Geopolitical Importance

South Korea's strategic importance is growing in America's strategy to contain China.
As a country with the most powerful manufacturing base in East Asia, it plays an important role in the supply chain.
From the U.S. perspective, South Korea is a key partner that cannot be completely replaced.

2. Strategy for Maintaining the South Korea-U.S. Alliance

Even within the Trump administration, relations with South Korea are strategically evaluated as an important alliance.
Defense cost-sharing negotiations are expected to be readjusted, and the U.S. is likely to increase its demands.
South Korea must establish a favorable negotiation strategy by linking the defense cost-sharing issue to economic benefits.

3. Economic Response Measures

Maintain solid cooperation with the U.S. through methods such as expanding investment in the U.S., increasing energy imports, and strengthening core technology cooperation.
Need to maximize South Korea's interests in a way that aligns with President Trump's economic policies.
Utilize FTAs and trade agreements to maintain strengthened economic cooperation with the U.S.

Global Impact of Trump's Second-Term Policies

1. Changes in the Global Trade Order

Increased possibility of trade decoupling with China (De-Coupling) due to Trump's strengthened protectionist trade policies.
The possibility of strengthening protectionism in major economic zones such as Europe and Japan, as well as the U.S., is emerging.

2. Manufacturing-Focused Policy and Opportunities for South Korean Companies

Due to President Trump's strategy to foster U.S. manufacturing, the need for local investment by South Korean companies is increasing.
South Korean companies are likely to benefit in the semiconductor, battery, and electric vehicle sectors.

3. Changes in Security and Military Cooperation

Expected increase in additional defense cost pressure on NATO allies, and South Korea may face similar pressure.
Instead of confirming the deployment of U.S. strategic assets, demands for increased military contributions from allies (e.g., demands for South Korea to increase its defense budget).

Strategic Response Directions South Korea Should Take

1. Efforts to Strengthen South Korea's Position in the South Korea-U.S. Alliance

A strategy to upgrade the "tier (level)" of the alliance is essential.
Refer to the fact that Japan successfully catered to President Trump's preferences during the Shinzo Abe administration (e.g., strengthening promotion of U.S.-Japan economic cooperation).
Induce strengthening South Korea's standing in the U.S. through economic support and a willingness to contribute to defense.

2. Increase Economic Cooperation with the U.S.

Expand investment in industrial fields that the U.S. values, such as semiconductors, AI, batteries, and the defense industry.
Actively consider plans to establish and expand production lines and investment in the U.S. that President Trump values.

Instead of simple monetary support, establish a "Win-Win" model through expanding cooperation between South Korean defense companies and the U.S. military industry.
Actively utilize alternative methods such as industrialization investment in U.S. military bases in South Korea and expanding maintenance of U.S. Forces Korea supplies.

4. Response to Supply Chain Restructuring

Reduce dependence on China and strengthen efforts to establish new production bases in Asia and the Americas.
Strengthen the role in the supply chain through expanding production facilities and R&D centers in the U.S.

< Summary >

President Trump's strategy: Intensification of competition between powerful nations, and continued strong pressure policies on allies.
South Korea's role: Maintaining its position as an essential partner for the U.S. in geopolitical, economic, and military aspects.
Economic response: Need to expand investment in the U.S., strengthen new industry cooperation, and increase South Korea's role in the supply chain.
Military response: Transform the defense cost issue into a strategic cooperation method rather than a financial burden.
Strengthening the South Korea-U.S. alliance: Promote a strategy to maximize South Korea's economic benefits by raising the alliance's "tier."