Spring mvc return http 404 with tomcat 7 servlet 3.0 and java 7

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I'm trying to config a java web project with spring mvc, and finally it will be upload to AWS. The environment is tomcat 7, servlet 3.0, java 7 with latest spring mvc 4.1.6

I followed a book called beginning spring from wrox press.

web.xml

<?xml version="1.0" encoding="UTF-8"?>
<web-app xmlns="http://ift.tt/nSRXKP"
    xmlns:xsi="http://ift.tt/ra1lAU"
    xsi:schemaLocation="http://ift.tt/nSRXKP
        http://ift.tt/1eWqHMP"
    version="3.0">
    <servlet>
        <servlet-name>mathschool</servlet-name>
        <servlet-class>
            org.springframework.web.servlet.DispatcherServlet
        </servlet-class>
        <load-on-startup>1</load-on-startup>
    </servlet>
    <servlet-mapping>
        <servlet-name>mathschool</servlet-name>
        <url-pattern>/</url-pattern>
    </servlet-mapping>
</web-app>

mathschool-servlet.xml

<?xml version="1.0" encoding="UTF-8"?>
<beans xmlns="http://ift.tt/GArMu6"
    xmlns:xsi="http://ift.tt/ra1lAU"
    xmlns:context="http://ift.tt/GArMu7"
    xsi:schemaLocation="http://ift.tt/GArMu6
        http://ift.tt/1cnl1uo
        http://ift.tt/GArMu7
        http://ift.tt/1ldEMZY">

    <context:component-scan base-package="sg.mathschool.controller" />
    <context:annotation-config />

    <bean class="org.springframework.web.servlet.view.InternalResourceViewResolver">
        <property name="prefix" value="/WEB-INF/jsp/" />
        <property name="suffix" value=".jsp" />
    </bean>
</beans>

pom.xml

<project 
    xmlns="http://ift.tt/IH78KX" 
    xmlns:xsi="http://ift.tt/ra1lAU" 
    xsi:schemaLocation="http://ift.tt/IH78KX 
        http://ift.tt/VE5zRx">

  <modelVersion>4.0.0</modelVersion>
  <groupId>MathSchool</groupId>
  <artifactId>MathSchool</artifactId>
  <version>0.0.1-SNAPSHOT</version>
  <packaging>war</packaging>
  <dependencies>
    <dependency>
      <groupId>com.amazonaws</groupId>
      <artifactId>aws-java-sdk</artifactId>
      <version>1.9.28.1</version>
    </dependency>
    <dependency>
      <groupId>org.springframework</groupId>
      <artifactId>spring-webmvc</artifactId>
      <version>4.1.6.RELEASE</version>
    </dependency>
  </dependencies>
  <build>
    <sourceDirectory>src</sourceDirectory>
    <plugins>
      <plugin>
        <artifactId>maven-compiler-plugin</artifactId>
        <version>3.1</version>
        <configuration>
          <source>1.7</source>
          <target>1.7</target>
        </configuration>
      </plugin>
      <plugin>
        <artifactId>maven-war-plugin</artifactId>
        <version>2.4</version>
        <configuration>
          <warSourceDirectory>WebContent</warSourceDirectory>
          <failOnMissingWebXml>false</failOnMissingWebXml>
        </configuration>
      </plugin>
    </plugins>
  </build>
</project>

HomeController

package sg.mathschool.controller;

import org.springframework.stereotype.Controller;
import org.springframework.web.bind.annotation.RequestMapping;
import org.springframework.web.bind.annotation.RequestMethod;

@Controller
public class HomeController {
    @RequestMapping(value = "/", method = RequestMethod.GET)
    public String index() {
        return "index";
    }
}

Project structure

However, I get this 404 always, I thought this is just a basic configuration to get a hello world application. What is wrong, and how can I get http://localhost:8080/ instead of http://localhost:8080/MathSchool/

asked 52 secs ago

Timeless

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Spring mvc return http 404 with tomcat 7 servlet 3.0 and java 7